diff --git a/applications/test/invTensor/Make/files b/applications/test/invTensor/Make/files
new file mode 100644
index 0000000000..c99507752a
--- /dev/null
+++ b/applications/test/invTensor/Make/files
@@ -0,0 +1,3 @@
+Test-invTensor.C
+
+EXE = $(FOAM_USER_APPBIN)/Test-invTensor
diff --git a/applications/test/invTensor/Make/options b/applications/test/invTensor/Make/options
new file mode 100644
index 0000000000..18e6fe47af
--- /dev/null
+++ b/applications/test/invTensor/Make/options
@@ -0,0 +1,2 @@
+/* EXE_INC = */
+/* EXE_LIBS = */
diff --git a/applications/test/invTensor/Test-invTensor.C b/applications/test/invTensor/Test-invTensor.C
new file mode 100644
index 0000000000..b16b7d3666
--- /dev/null
+++ b/applications/test/invTensor/Test-invTensor.C
@@ -0,0 +1,96 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2023 OpenCFD Ltd.
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Application
+    Test-invTensor
+
+Description
+    Tests for regular and corner cases of tensor inversion.
+
+\*---------------------------------------------------------------------------*/
+
+#include "tensor.H"
+#include "symmTensor.H"
+#include "transform.H"
+#include "unitConversion.H"
+#include "Random.H"
+#include "scalar.H"
+#include "complex.H"
+#include "sigFpe.H"
+
+using namespace Foam;
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+template<class TensorType>
+void test_invert(const TensorType& tt)
+{
+    Info<< pTraits<TensorType>::typeName << nl
+        << "ten : " << tt << nl;
+
+    // Non-failsafe. try/catch does not work here
+    if (tt.det() < ROOTVSMALL)
+    {
+        Info<< "inv : " << "nan/inf" << nl;
+    }
+    else
+    {
+        Info<< "inv : " << tt.inv() << nl;
+    }
+
+    // Failsafe
+    Info<< "inv : " << tt.safeInv() << nl;
+
+    Info<< nl;
+}
+
+
+// * * * * * * * * * * * * * * * Main Program  * * * * * * * * * * * * * * * //
+
+int main(int argc, char *argv[])
+{
+    // Run with FOAM_SIGFPE=true to ensure we see divide by zero
+    Foam::sigFpe::set(true);
+
+    {
+        symmTensor st(1e-3, 0, 0, 1e-3, 0, 1e-6);
+        test_invert(st);
+    }
+
+    {
+        symmTensor st(1e-3, 0, 0, 1e-3, 0, 1e-30);
+        test_invert(st);
+    }
+
+    {
+        symmTensor st(1e-3, 0, 0, 1e-3, 0, 0);
+        test_invert(st);
+    }
+
+    return 0;
+}
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
diff --git a/src/OpenFOAM/dimensionedTypes/dimensionedSymmTensor/dimensionedSymmTensor.H b/src/OpenFOAM/dimensionedTypes/dimensionedSymmTensor/dimensionedSymmTensor.H
index 2d7cbf6016..a435341551 100644
--- a/src/OpenFOAM/dimensionedTypes/dimensionedSymmTensor/dimensionedSymmTensor.H
+++ b/src/OpenFOAM/dimensionedTypes/dimensionedSymmTensor/dimensionedSymmTensor.H
@@ -50,7 +50,7 @@ namespace Foam
 typedef dimensioned<symmTensor> dimensionedSymmTensor;
 
 
-// global functions
+// Global Functions
 
 dimensionedSymmTensor sqr(const dimensionedVector&);
 dimensionedSymmTensor innerSqr(const dimensionedSymmTensor&);
@@ -65,7 +65,7 @@ dimensionedSymmTensor cof(const dimensionedSymmTensor&);
 dimensionedSymmTensor inv(const dimensionedSymmTensor&);
 
 
-// global operators
+// Global Operators
 
 //- Hodge Dual operator (tensor -> vector)
 dimensionedVector operator*(const dimensionedSymmTensor&);
diff --git a/src/OpenFOAM/dimensionedTypes/dimensionedTensor/dimensionedTensor.H b/src/OpenFOAM/dimensionedTypes/dimensionedTensor/dimensionedTensor.H
index 8de0683efe..a66aea3c07 100644
--- a/src/OpenFOAM/dimensionedTypes/dimensionedTensor/dimensionedTensor.H
+++ b/src/OpenFOAM/dimensionedTypes/dimensionedTensor/dimensionedTensor.H
@@ -51,8 +51,7 @@ namespace Foam
 
 typedef dimensioned<tensor> dimensionedTensor;
 
-
-// global functions
+// Global Functions
 
 dimensionedScalar tr(const dimensionedTensor&);
 dimensionedTensor dev(const dimensionedTensor&);
@@ -68,7 +67,7 @@ dimensionedVector eigenValues(const dimensionedSymmTensor&);
 dimensionedTensor eigenVectors(const dimensionedSymmTensor&);
 
 
-// global operators
+// Global Operators
 
 //- Hodge Dual operator (tensor -> vector)
 dimensionedVector operator*(const dimensionedTensor&);
diff --git a/src/OpenFOAM/fields/Fields/symmTensorField/symmTensorField.C b/src/OpenFOAM/fields/Fields/symmTensorField/symmTensorField.C
index 1be5183d4c..afdf86c186 100644
--- a/src/OpenFOAM/fields/Fields/symmTensorField/symmTensorField.C
+++ b/src/OpenFOAM/fields/Fields/symmTensorField/symmTensorField.C
@@ -51,55 +51,10 @@ UNARY_FUNCTION(symmTensor, symmTensor, dev2)
 UNARY_FUNCTION(scalar, symmTensor, det)
 UNARY_FUNCTION(symmTensor, symmTensor, cof)
 
-void inv(Field<symmTensor>& result, const UList<symmTensor>& tf1)
+void inv(Field<symmTensor>& result, const UList<symmTensor>& f1)
 {
-    if (result.empty() || tf1.empty())
-    {
-        return;
-    }
-
-    // Attempting to identify 2-D cases
-    const scalar minThreshold = SMALL * magSqr(tf1[0]);
-
-    const bool small_xx = (magSqr(tf1[0].xx()) < minThreshold);
-    const bool small_yy = (magSqr(tf1[0].yy()) < minThreshold);
-    const bool small_zz = (magSqr(tf1[0].zz()) < minThreshold);
-
-    if (small_xx || small_yy || small_zz)
-    {
-        const vector adjust
-        (
-            (small_xx ? 1 : 0),
-            (small_yy ? 1 : 0),
-            (small_zz ? 1 : 0)
-        );
-
-        // Cannot use TFOR_ALL_F_OP_FUNC_F (additional operations)
-
-        const label loopLen = (result).size();
-
-        /* pragmas... */
-        for (label i = 0; i < loopLen; ++i)
-        {
-            symmTensor work(tf1[i]);
-            work.addDiag(adjust);
-
-            result[i] = Foam::inv(work);
-            result[i].subtractDiag(adjust);
-        }
-    }
-    else
-    {
-        // Same as TFOR_ALL_F_OP_FUNC_F
-
-        const label loopLen = (result).size();
-
-        /* pragmas... */
-        for (label i = 0; i < loopLen; ++i)
-        {
-            result[i] = Foam::inv(tf1[i]);
-        }
-    }
+    // With 'failsafe' invert
+    TFOR_ALL_F_OP_F_FUNC(symmTensor, result, =, symmTensor, f1, safeInv)
 }
 
 tmp<symmTensorField> inv(const UList<symmTensor>& tf)
diff --git a/src/OpenFOAM/fields/Fields/tensorField/tensorField.C b/src/OpenFOAM/fields/Fields/tensorField/tensorField.C
index c4f76fc978..9b343fa5a0 100644
--- a/src/OpenFOAM/fields/Fields/tensorField/tensorField.C
+++ b/src/OpenFOAM/fields/Fields/tensorField/tensorField.C
@@ -50,55 +50,10 @@ UNARY_FUNCTION(tensor, tensor, dev2)
 UNARY_FUNCTION(scalar, tensor, det)
 UNARY_FUNCTION(tensor, tensor, cof)
 
-void inv(Field<tensor>& result, const UList<tensor>& tf1)
+void inv(Field<tensor>& result, const UList<tensor>& f1)
 {
-    if (result.empty() || tf1.empty())
-    {
-        return;
-    }
-
-    // Attempting to identify 2-D cases
-    const scalar minThreshold = SMALL * magSqr(tf1[0]);
-
-    const bool small_xx = (magSqr(tf1[0].xx()) < minThreshold);
-    const bool small_yy = (magSqr(tf1[0].yy()) < minThreshold);
-    const bool small_zz = (magSqr(tf1[0].zz()) < minThreshold);
-
-    if (small_xx || small_yy || small_zz)
-    {
-        const vector adjust
-        (
-            (small_xx ? 1 : 0),
-            (small_yy ? 1 : 0),
-            (small_zz ? 1 : 0)
-        );
-
-        // Cannot use TFOR_ALL_F_OP_FUNC_F (additional operations)
-
-        const label loopLen = (result).size();
-
-        /* pragmas... */
-        for (label i = 0; i < loopLen; ++i)
-        {
-            tensor work(tf1[i]);
-            work.addDiag(adjust);
-
-            result[i] = Foam::inv(work);
-            result[i].subtractDiag(adjust);
-        }
-    }
-    else
-    {
-        // Same as TFOR_ALL_F_OP_FUNC_F
-
-        const label loopLen = (result).size();
-
-        /* pragmas... */
-        for (label i = 0; i < loopLen; ++i)
-        {
-            result[i] = Foam::inv(tf1[i]);
-        }
-    }
+    // With 'failsafe' invert
+    TFOR_ALL_F_OP_F_FUNC(tensor, result, =, tensor, f1, safeInv)
 }
 
 tmp<tensorField> inv(const UList<tensor>& tf)
diff --git a/src/OpenFOAM/primitives/SymmTensor/SymmTensor.H b/src/OpenFOAM/primitives/SymmTensor/SymmTensor.H
index e365081023..2f38d3e481 100644
--- a/src/OpenFOAM/primitives/SymmTensor/SymmTensor.H
+++ b/src/OpenFOAM/primitives/SymmTensor/SymmTensor.H
@@ -245,15 +245,20 @@ public:
         //- The 2D determinant by excluding given direction
         inline Cmpt det2D(const direction excludeCmpt) const;
 
-        //- Return cofactor matrix
+        //- Return adjunct matrix (transpose of cofactor matrix)
+        inline SymmTensor<Cmpt> adjunct() const;
+
+        //- Return cofactor matrix (transpose of adjunct matrix)
         inline SymmTensor<Cmpt> cof() const;
 
-        //- Return 2D cofactor matrix by excluding given direction
-        inline SymmTensor<Cmpt> cof2D(const direction excludeCmpt) const;
+        //- Return 2D adjunct matrix by excluding given direction
+        inline SymmTensor<Cmpt> adjunct2D(const direction excludeCmpt) const;
 
-        //- Return inverse, with optional (ad hoc) failsafe handling
-        //- of 2D tensors
-        inline SymmTensor<Cmpt> inv(const bool failsafe=false) const;
+        //- Return inverse
+        inline SymmTensor<Cmpt> inv() const;
+
+        //- Return inverse, with (ad hoc) failsafe handling of 2D tensors
+        inline SymmTensor<Cmpt> safeInv() const;
 
         //- Return inverse of 2D tensor (by excluding given direction)
         inline SymmTensor<Cmpt> inv2D(const direction excludeCmpt) const;
diff --git a/src/OpenFOAM/primitives/SymmTensor/SymmTensorI.H b/src/OpenFOAM/primitives/SymmTensor/SymmTensorI.H
index 47c10fa13b..5c28c6c2bc 100644
--- a/src/OpenFOAM/primitives/SymmTensor/SymmTensorI.H
+++ b/src/OpenFOAM/primitives/SymmTensor/SymmTensorI.H
@@ -272,24 +272,28 @@ inline Cmpt Foam::SymmTensor<Cmpt>::det2D(const direction excludeCmpt) const
 
 
 template<class Cmpt>
-inline Foam::SymmTensor<Cmpt> Foam::SymmTensor<Cmpt>::cof() const
+inline Foam::SymmTensor<Cmpt> Foam::SymmTensor<Cmpt>::adjunct() const
 {
+    // symmetric: cof() == adjunct()
     return SymmTensor<Cmpt>
     (
-        yy()*zz() - yz()*yz(),
-        xz()*yz() - xy()*zz(),
-        xy()*yz() - xz()*yy(),
-
-        xx()*zz() - xz()*xz(),
-        xy()*xz() - xx()*yz(),
-
-        xx()*yy() - xy()*xy()
+        yy()*zz() - yz()*yz(), xz()*yz() - xy()*zz(), xy()*yz() - xz()*yy(),
+                               xx()*zz() - xz()*xz(), xy()*xz() - xx()*yz(),
+                                                      xx()*yy() - xy()*xy()
     );
 }
 
 
 template<class Cmpt>
-inline Foam::SymmTensor<Cmpt> Foam::SymmTensor<Cmpt>::cof2D
+inline Foam::SymmTensor<Cmpt> Foam::SymmTensor<Cmpt>::cof() const
+{
+    // symmetric: cof() == adjunct()
+    return this->adjunct();
+}
+
+
+template<class Cmpt>
+inline Foam::SymmTensor<Cmpt> Foam::SymmTensor<Cmpt>::adjunct2D
 (
     const direction excludeCmpt
 ) const
@@ -335,7 +339,84 @@ inline Foam::SymmTensor<Cmpt> Foam::SymmTensor<Cmpt>::inv2D
 {
     const Cmpt detval = this->det2D(excludeCmpt);
 
-    return this->cof2D(excludeCmpt).T()/detval;
+    return this->adjunct2D(excludeCmpt)/detval;
+}
+
+
+// Invert without much error handling
+template<class Cmpt>
+inline Foam::SymmTensor<Cmpt> Foam::SymmTensor<Cmpt>::inv() const
+{
+    const Cmpt detval = this->det();
+
+    #ifdef FULLDEBUG
+    if (mag(detval) < VSMALL)
+    {
+        FatalErrorInFunction
+            << "Tensor not properly invertible, determinant:"
+            << detval << " tensor:" << *this << nl
+            << abort(FatalError);
+    }
+    #endif
+
+    return this->adjunct()/detval;
+}
+
+
+// Invert with some error handling
+template<class Cmpt>
+inline Foam::SymmTensor<Cmpt> Foam::SymmTensor<Cmpt>::safeInv() const
+{
+    {
+        // Attempt to identify and handle 2-D cases.
+        // - use diagSqr instead of magSqr for fewer operations
+        const scalar magSqr_xx = Foam::magSqr(xx());
+        const scalar magSqr_yy = Foam::magSqr(yy());
+        const scalar magSqr_zz = Foam::magSqr(zz());
+
+        // SMALL: 1e-15 (double), 1e-6 (float), but 1e-6 may be adequate
+
+        const scalar threshold = SMALL * (magSqr_xx + magSqr_yy + magSqr_zz);
+
+        const bool small_xx = (magSqr_xx < threshold);
+        const bool small_yy = (magSqr_yy < threshold);
+        const bool small_zz = (magSqr_zz < threshold);
+
+        if (small_xx || small_yy || small_zz)
+        {
+            SymmTensor<Cmpt> work(*this);
+
+            if (small_xx) { work.xx() += pTraits<Cmpt>::one; }
+            if (small_yy) { work.yy() += pTraits<Cmpt>::one; }
+            if (small_zz) { work.zz() += pTraits<Cmpt>::one; }
+
+            const Cmpt detval = work.det();
+
+            if (mag(detval) < ROOTVSMALL)
+            {
+                // Appears to be nearly zero - leave untouched?
+                return SymmTensor<Cmpt>(Zero);
+            }
+
+            work = work.adjunct()/detval;
+
+            if (small_xx) { work.xx() -= pTraits<Cmpt>::one; }
+            if (small_yy) { work.yy() -= pTraits<Cmpt>::one; }
+            if (small_zz) { work.zz() -= pTraits<Cmpt>::one; }
+
+            return work;
+        }
+    }
+
+    const Cmpt detval = this->det();
+
+    if (mag(detval) < ROOTVSMALL)
+    {
+        // Appears to be nearly zero - leave untouched?
+        return SymmTensor<Cmpt>(Zero);
+    }
+
+    return this->adjunct()/detval;
 }
 
 
@@ -438,7 +519,7 @@ inline SymmTensor<Cmpt> inv(const SymmTensor<Cmpt>& st, const Cmpt detval)
     }
     #endif
 
-    return st.cof().T()/detval;
+    return st.adjunct()/detval;
 }
 
 
@@ -446,62 +527,7 @@ inline SymmTensor<Cmpt> inv(const SymmTensor<Cmpt>& st, const Cmpt detval)
 template<class Cmpt>
 inline SymmTensor<Cmpt> inv(const SymmTensor<Cmpt>& st)
 {
-    return inv(st, st.det());
-}
-
-
-template<class Cmpt>
-inline SymmTensor<Cmpt> SymmTensor<Cmpt>::inv(const bool failsafe) const
-{
-    const Cmpt detval = this->det();
-
-    if (failsafe)
-    {
-        // Attempt to identify and handle 2-D cases.
-        // - use diagSqr instead of magSqr for fewer operations
-        const scalar magSqr_xx = Foam::magSqr(xx());
-        const scalar magSqr_yy = Foam::magSqr(yy());
-        const scalar magSqr_zz = Foam::magSqr(zz());
-
-        const scalar threshold = SMALL * (magSqr_xx + magSqr_yy + magSqr_zz);
-
-        const bool small_xx = (magSqr_xx < threshold);
-        const bool small_yy = (magSqr_yy < threshold);
-        const bool small_zz = (magSqr_zz < threshold);
-
-        if (small_xx || small_yy || small_zz)
-        {
-            SymmTensor<Cmpt> work(*this);
-
-            if (small_xx) { work.xx() += pTraits<Cmpt>::one; }
-            if (small_yy) { work.yy() += pTraits<Cmpt>::one; }
-            if (small_zz) { work.zz() += pTraits<Cmpt>::one; }
-
-            work = Foam::inv(work, work.det());
-
-            if (small_xx) { work.xx() -= pTraits<Cmpt>::one; }
-            if (small_yy) { work.yy() -= pTraits<Cmpt>::one; }
-            if (small_zz) { work.zz() -= pTraits<Cmpt>::one; }
-
-            return work;
-        }
-        else if (mag(detval) < VSMALL)
-        {
-            // Really appears to be zero - leave untouched?
-            return SymmTensor<Cmpt>(Zero);
-        }
-    }
-    #ifdef FULLDEBUG
-    else if (mag(detval) < VSMALL)
-    {
-        FatalErrorInFunction
-            << "Tensor not properly invertible, determinant:"
-            << detval << " tensor:" << *this << nl
-            << abort(FatalError);
-    }
-    #endif
-
-    return this->cof().T()/detval;
+    return st.inv();
 }
 
 
diff --git a/src/OpenFOAM/primitives/SymmTensor/symmTensor/symmTensor.C b/src/OpenFOAM/primitives/SymmTensor/symmTensor/symmTensor.C
index 8869e9fb56..fb41001b1f 100644
--- a/src/OpenFOAM/primitives/SymmTensor/symmTensor/symmTensor.C
+++ b/src/OpenFOAM/primitives/SymmTensor/symmTensor/symmTensor.C
@@ -340,9 +340,9 @@ Foam::tensor Foam::eigenVectors(const symmTensor& T)
 
 Foam::symmTensor Foam::pinv(const symmTensor& st)
 {
-    const scalar dt = det(st);
+    const scalar detval = st.det();
 
-    if (dt < ROOTVSMALL)
+    if (detval < ROOTVSMALL)
     {
         // Fall back to pseudo inverse
         scalarRectangularMatrix mat(3, 3);
@@ -361,7 +361,7 @@ Foam::symmTensor Foam::pinv(const symmTensor& st)
         );
     }
 
-    return inv(st, dt);
+    return Foam::inv(st, detval);
 }
 
 
diff --git a/src/OpenFOAM/primitives/SymmTensor2D/SymmTensor2D.H b/src/OpenFOAM/primitives/SymmTensor2D/SymmTensor2D.H
index 1308b015e9..e70a951c9b 100644
--- a/src/OpenFOAM/primitives/SymmTensor2D/SymmTensor2D.H
+++ b/src/OpenFOAM/primitives/SymmTensor2D/SymmTensor2D.H
@@ -152,7 +152,10 @@ public:
         //- The determinate
         inline Cmpt det() const;
 
-        //- Return cofactor matrix
+        //- Return adjunct matrix (transpose of cofactor matrix)
+        inline SymmTensor2D<Cmpt> adjunct() const;
+
+        //- Return cofactor matrix (transpose of adjunct matrix)
         inline SymmTensor2D<Cmpt> cof() const;
 
         //- Return inverse
diff --git a/src/OpenFOAM/primitives/SymmTensor2D/SymmTensor2DI.H b/src/OpenFOAM/primitives/SymmTensor2D/SymmTensor2DI.H
index b583b669c5..4eba6e6cc3 100644
--- a/src/OpenFOAM/primitives/SymmTensor2D/SymmTensor2DI.H
+++ b/src/OpenFOAM/primitives/SymmTensor2D/SymmTensor2DI.H
@@ -109,16 +109,45 @@ inline Cmpt Foam::SymmTensor2D<Cmpt>::det() const
 
 
 template<class Cmpt>
-inline Foam::SymmTensor2D<Cmpt> Foam::SymmTensor2D<Cmpt>::cof() const
+inline Foam::SymmTensor2D<Cmpt> Foam::SymmTensor2D<Cmpt>::adjunct() const
 {
+    // symmetric: cof() == adjunct()
     return SymmTensor2D<Cmpt>
     (
-        yy(), -yx(),
+        yy(), -xy(),
                xx()
     );
 }
 
 
+template<class Cmpt>
+inline Foam::SymmTensor2D<Cmpt> Foam::SymmTensor2D<Cmpt>::cof() const
+{
+    // symmetric: cof() == adjunct()
+    return this->adjunct();
+}
+
+
+// Invert without much error handling
+template<class Cmpt>
+inline Foam::SymmTensor2D<Cmpt> Foam::SymmTensor2D<Cmpt>::inv() const
+{
+    const Cmpt detval = this->det();
+
+    #ifdef FULLDEBUG
+    if (mag(detval) < SMALL)
+    {
+        FatalErrorInFunction
+            << "SymmTensor2D not properly invertible, determinant:"
+            << detval << " tensor:" << *this << nl
+            << abort(FatalError);
+    }
+    #endif
+
+    return this->adjunct()/detval;
+}
+
+
 // * * * * * * * * * * * * * * * Member Operators  * * * * * * * * * * * * * //
 
 template<class Cmpt>
@@ -220,7 +249,7 @@ inline SymmTensor2D<Cmpt> inv(const SymmTensor2D<Cmpt>& st, const Cmpt detval)
     }
     #endif
 
-    return st.cof().T()/detval;
+    return st.adjunct()/detval;
 }
 
 
@@ -228,15 +257,7 @@ inline SymmTensor2D<Cmpt> inv(const SymmTensor2D<Cmpt>& st, const Cmpt detval)
 template<class Cmpt>
 inline SymmTensor2D<Cmpt> inv(const SymmTensor2D<Cmpt>& st)
 {
-    return inv(st, st.det());
-}
-
-
-// The inverse of this SymmTensor2D
-template<class Cmpt>
-inline SymmTensor2D<Cmpt> SymmTensor2D<Cmpt>::inv() const
-{
-    return Foam::inv(*this, this->det());
+    return st.inv();
 }
 
 
diff --git a/src/OpenFOAM/primitives/Tensor/Tensor.H b/src/OpenFOAM/primitives/Tensor/Tensor.H
index 7391d06865..601e004416 100644
--- a/src/OpenFOAM/primitives/Tensor/Tensor.H
+++ b/src/OpenFOAM/primitives/Tensor/Tensor.H
@@ -287,15 +287,20 @@ public:
         //- The 2D determinant by excluding given direction
         inline Cmpt det2D(const direction excludeCmpt) const;
 
-        //- Return cofactor matrix
+        //- Return adjunct matrix (transpose of cofactor matrix)
+        inline Tensor<Cmpt> adjunct() const;
+
+        //- Return cofactor matrix (transpose of adjunct matrix)
         inline Tensor<Cmpt> cof() const;
 
-        //- Return 2D cofactor matrix by excluding given direction
-        inline Tensor<Cmpt> cof2D(const direction excludeCmpt) const;
+        //- Return 2D adjunct matrix by excluding given direction
+        inline Tensor<Cmpt> adjunct2D(const direction excludeCmpt) const;
 
-        //- Return inverse, with optional (ad hoc) failsafe handling
-        //- of 2D tensors
-        inline Tensor<Cmpt> inv(const bool failsafe=false) const;
+        //- Return inverse
+        inline Tensor<Cmpt> inv() const;
+
+        //- Return inverse, with (ad hoc) failsafe handling of 2D tensors
+        inline Tensor<Cmpt> safeInv() const;
 
         //- Return inverse of 2D tensor (by excluding given direction)
         inline Tensor<Cmpt> inv2D(const direction excludeCmpt) const;
diff --git a/src/OpenFOAM/primitives/Tensor/TensorI.H b/src/OpenFOAM/primitives/Tensor/TensorI.H
index 6e24c0f506..b389f12ee1 100644
--- a/src/OpenFOAM/primitives/Tensor/TensorI.H
+++ b/src/OpenFOAM/primitives/Tensor/TensorI.H
@@ -468,27 +468,26 @@ inline Cmpt Foam::Tensor<Cmpt>::det2D(const direction excludeCmpt) const
 
 
 template<class Cmpt>
-inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::cof() const
+inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::adjunct() const
 {
     return Tensor<Cmpt>
     (
-        yy()*zz() - zy()*yz(),
-        zx()*yz() - yx()*zz(),
-        yx()*zy() - yy()*zx(),
-
-        xz()*zy() - xy()*zz(),
-        xx()*zz() - xz()*zx(),
-        xy()*zx() - xx()*zy(),
-
-        xy()*yz() - xz()*yy(),
-        yx()*xz() - xx()*yz(),
-        xx()*yy() - yx()*xy()
+        yy()*zz() - zy()*yz(), xz()*zy() - xy()*zz(), xy()*yz() - xz()*yy(),
+        zx()*yz() - yx()*zz(), xx()*zz() - xz()*zx(), yx()*xz() - xx()*yz(),
+        yx()*zy() - yy()*zx(), xy()*zx() - xx()*zy(), xx()*yy() - yx()*xy()
     );
 }
 
 
 template<class Cmpt>
-inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::cof2D
+inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::cof() const
+{
+    return this->adjunct().T();
+}
+
+
+template<class Cmpt>
+inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::adjunct2D
 (
     const direction excludeCmpt
 ) const
@@ -500,8 +499,8 @@ inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::cof2D
             return Tensor<Cmpt>
             (
                 Zero,  Zero,  Zero,
-                Zero,  zz(), -zy(),
-                Zero, -yz(),  yy()
+                Zero,  zz(), -yz(),
+                Zero, -zy(),  yy()
             );
         }
 
@@ -509,9 +508,9 @@ inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::cof2D
         {
             return Tensor<Cmpt>
             (
-                zz(), Zero, -zx(),
+                zz(), Zero, -xz(),
                 Zero, Zero,  Zero,
-               -xz(), Zero,  xx()
+               -zx(), Zero,  xx()
             );
         }
     }
@@ -519,8 +518,8 @@ inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::cof2D
     // Fall-through: Eliminate z
     return Tensor<Cmpt>
     (
-        yy(), -yx(), Zero,
-       -xy(),  xx(), Zero,
+        yy(), -xy(), Zero,
+       -yx(),  xx(), Zero,
         Zero,  Zero, Zero
     );
 }
@@ -534,7 +533,7 @@ inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::inv2D
 {
     const Cmpt detval = this->det2D(excludeCmpt);
 
-    return this->cof2D(excludeCmpt).T()/detval;
+    return this->adjunct2D(excludeCmpt)/detval;
 }
 
 
@@ -576,6 +575,84 @@ Foam::Tensor<Cmpt>::schur(const Tensor<Cmpt>& t2) const
 }
 
 
+// Invert without much error handling
+template<class Cmpt>
+inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::inv() const
+{
+    const Cmpt detval = this->det();
+
+    #ifdef FULLDEBUG
+    if (mag(detval) < VSMALL)
+    {
+        FatalErrorInFunction
+            << "Tensor not properly invertible, determinant:"
+            << detval << " tensor:" << *this << nl
+            << abort(FatalError);
+    }
+    #endif
+
+    return this->adjunct()/detval;
+}
+
+
+// Invert with some error handling
+template<class Cmpt>
+inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::safeInv() const
+{
+    {
+        // Attempt to identify and handle 2-D cases
+        // - use diagSqr instead of magSqr for fewer operations
+
+        const scalar magSqr_xx = Foam::magSqr(xx());
+        const scalar magSqr_yy = Foam::magSqr(yy());
+        const scalar magSqr_zz = Foam::magSqr(zz());
+
+        // SMALL: 1e-15 (double), 1e-6 (float), but 1e-6 may be adequate
+
+        const scalar threshold = SMALL * (magSqr_xx + magSqr_yy + magSqr_zz);
+
+        const bool small_xx = (magSqr_xx < threshold);
+        const bool small_yy = (magSqr_yy < threshold);
+        const bool small_zz = (magSqr_zz < threshold);
+
+        if (small_xx || small_yy || small_zz)
+        {
+            Tensor<Cmpt> work(*this);
+
+            if (small_xx) { work.xx() += pTraits<Cmpt>::one; }
+            if (small_yy) { work.yy() += pTraits<Cmpt>::one; }
+            if (small_zz) { work.zz() += pTraits<Cmpt>::one; }
+
+            const Cmpt detval = work.det();
+
+            if (mag(detval) < ROOTVSMALL)
+            {
+                // Appears to be nearly zero - leave untouched?
+                return Tensor<Cmpt>(Zero);
+            }
+
+            work = work.adjunct()/detval;
+
+            if (small_xx) { work.xx() -= pTraits<Cmpt>::one; }
+            if (small_yy) { work.yy() -= pTraits<Cmpt>::one; }
+            if (small_zz) { work.zz() -= pTraits<Cmpt>::one; }
+
+            return work;
+        }
+    }
+
+    const Cmpt detval = this->det();
+
+    if (mag(detval) < ROOTVSMALL)
+    {
+        // Appears to be nearly zero - leave untouched?
+        return Tensor<Cmpt>(Zero);
+    }
+
+    return this->adjunct()/detval;
+}
+
+
 // * * * * * * * * * * * * * * * Member Operators  * * * * * * * * * * * * * //
 
 template<class Cmpt>
@@ -750,7 +827,7 @@ inline Tensor<Cmpt> inv(const Tensor<Cmpt>& t, const Cmpt detval)
     }
     #endif
 
-    return t.cof().T()/detval;
+    return t.adjunct()/detval;
 }
 
 
@@ -758,63 +835,7 @@ inline Tensor<Cmpt> inv(const Tensor<Cmpt>& t, const Cmpt detval)
 template<class Cmpt>
 inline Tensor<Cmpt> inv(const Tensor<Cmpt>& t)
 {
-    return inv(t, t.det());
-}
-
-
-template<class Cmpt>
-inline Tensor<Cmpt> Tensor<Cmpt>::inv(const bool failsafe) const
-{
-    const Cmpt detval = this->det();
-
-    if (failsafe)
-    {
-        // Attempt to identify and handle 2-D cases
-        // - use diagSqr instead of magSqr for fewer operations
-
-        const scalar magSqr_xx = Foam::magSqr(xx());
-        const scalar magSqr_yy = Foam::magSqr(yy());
-        const scalar magSqr_zz = Foam::magSqr(zz());
-
-        const scalar threshold = SMALL * (magSqr_xx + magSqr_yy + magSqr_zz);
-
-        const bool small_xx = (magSqr_xx < threshold);
-        const bool small_yy = (magSqr_yy < threshold);
-        const bool small_zz = (magSqr_zz < threshold);
-
-        if (small_xx || small_yy || small_zz)
-        {
-            Tensor<Cmpt> work(*this);
-
-            if (small_xx) { work.xx() += pTraits<Cmpt>::one; }
-            if (small_yy) { work.yy() += pTraits<Cmpt>::one; }
-            if (small_zz) { work.zz() += pTraits<Cmpt>::one; }
-
-            work = Foam::inv(work, work.det());
-
-            if (small_xx) { work.xx() -= pTraits<Cmpt>::one; }
-            if (small_yy) { work.yy() -= pTraits<Cmpt>::one; }
-            if (small_zz) { work.zz() -= pTraits<Cmpt>::one; }
-
-            return work;
-        }
-        else if (mag(detval) < VSMALL)
-        {
-            // Really appears to be zero - leave untouched?
-            return Tensor<Cmpt>(Zero);
-        }
-    }
-    #ifdef FULLDEBUG
-    else if (mag(detval) < VSMALL)
-    {
-        FatalErrorInFunction
-            << "Tensor not properly invertible, determinant:"
-            << detval << " tensor:" << *this << nl
-            << abort(FatalError);
-    }
-    #endif
-
-    return this->cof().T()/detval;
+    return t.inv();
 }
 
 
diff --git a/src/OpenFOAM/primitives/Tensor/floats/tensor.C b/src/OpenFOAM/primitives/Tensor/floats/tensor.C
index dfe5851bd0..d26aad40a4 100644
--- a/src/OpenFOAM/primitives/Tensor/floats/tensor.C
+++ b/src/OpenFOAM/primitives/Tensor/floats/tensor.C
@@ -304,9 +304,9 @@ Foam::Tensor<Foam::complex> Foam::eigenVectors(const tensor& T)
 
 Foam::tensor Foam::pinv(const tensor& t)
 {
-    const scalar dt = det(t);
+    const scalar detval = t.det();
 
-    if (dt < ROOTVSMALL)
+    if (detval < ROOTVSMALL)
     {
         // Fall back to pseudo inverse
         scalarRectangularMatrix mat(3, 3);
@@ -325,7 +325,7 @@ Foam::tensor Foam::pinv(const tensor& t)
         );
     }
 
-    return inv(t, dt);
+    return Foam::inv(t, detval);
 }
 
 
diff --git a/src/OpenFOAM/primitives/Tensor2D/Tensor2D.H b/src/OpenFOAM/primitives/Tensor2D/Tensor2D.H
index f12b68104f..69f8efd091 100644
--- a/src/OpenFOAM/primitives/Tensor2D/Tensor2D.H
+++ b/src/OpenFOAM/primitives/Tensor2D/Tensor2D.H
@@ -212,7 +212,10 @@ public:
         //- The determinate
         inline Cmpt det() const;
 
-        //- Return cofactor matrix
+        //- Return adjunct matrix (transpose of cofactor matrix)
+        inline Tensor2D<Cmpt> adjunct() const;
+
+        //- Return cofactor matrix (transpose of adjunct matrix)
         inline Tensor2D<Cmpt> cof() const;
 
         //- Return inverse
diff --git a/src/OpenFOAM/primitives/Tensor2D/Tensor2DI.H b/src/OpenFOAM/primitives/Tensor2D/Tensor2DI.H
index 9367f4c82b..1acbb876a8 100644
--- a/src/OpenFOAM/primitives/Tensor2D/Tensor2DI.H
+++ b/src/OpenFOAM/primitives/Tensor2D/Tensor2DI.H
@@ -318,16 +318,23 @@ inline Cmpt Foam::Tensor2D<Cmpt>::det() const
 
 
 template<class Cmpt>
-inline Foam::Tensor2D<Cmpt> Foam::Tensor2D<Cmpt>::cof() const
+inline Foam::Tensor2D<Cmpt> Foam::Tensor2D<Cmpt>::adjunct() const
 {
     return Tensor2D<Cmpt>
     (
-        yy(), -yx(),
-       -xy(),  xx()
+        yy(), -xy(),
+       -yx(),  xx()
     );
 }
 
 
+template<class Cmpt>
+inline Foam::Tensor2D<Cmpt> Foam::Tensor2D<Cmpt>::cof() const
+{
+    return this->adjunct().T();
+}
+
+
 template<class Cmpt>
 inline Foam::Tensor2D<Cmpt>
 Foam::Tensor2D<Cmpt>::inner(const Tensor2D<Cmpt>& t2) const
@@ -359,6 +366,26 @@ Foam::Tensor2D<Cmpt>::schur(const Tensor2D<Cmpt>& t2) const
 }
 
 
+// Invert without much error handling
+template<class Cmpt>
+inline Foam::Tensor2D<Cmpt> Foam::Tensor2D<Cmpt>::inv() const
+{
+    const Cmpt detval = this->det();
+
+    #ifdef FULLDEBUG
+    if (mag(detval) < SMALL)
+    {
+        FatalErrorInFunction
+            << "SymmTensor2D not properly invertible, determinant:"
+            << detval << " tensor:" << *this << nl
+            << abort(FatalError);
+    }
+    #endif
+
+    return this->adjunct()/detval;
+}
+
+
 // * * * * * * * * * * * * * * * Member Operators  * * * * * * * * * * * * * //
 
 template<class Cmpt>
@@ -463,7 +490,7 @@ inline Cmpt det(const Tensor2D<Cmpt>& t)
 }
 
 
-//- Return the cofactor Tensor2D of a Tensor2D
+//- Return the cofactor of a Tensor2D
 template<class Cmpt>
 inline Tensor2D<Cmpt> cof(const Tensor2D<Cmpt>& t)
 {
@@ -485,7 +512,7 @@ inline Tensor2D<Cmpt> inv(const Tensor2D<Cmpt>& t, const Cmpt detval)
     }
     #endif
 
-    return t.cof().T()/detval;
+    return t.adjunct()/detval;
 }
 
 
@@ -493,15 +520,7 @@ inline Tensor2D<Cmpt> inv(const Tensor2D<Cmpt>& t, const Cmpt detval)
 template<class Cmpt>
 inline Tensor2D<Cmpt> inv(const Tensor2D<Cmpt>& t)
 {
-    return inv(t, t.det());
-}
-
-
-// Return the inverse of this Tensor2D
-template<class Cmpt>
-inline Tensor2D<Cmpt> Tensor2D<Cmpt>::inv() const
-{
-    return Foam::inv(*this, this->det());
+    return t.inv();
 }
 
 
diff --git a/src/finiteArea/finiteArea/gradSchemes/leastSquaresFaGrad/leastSquaresFaVectors.C b/src/finiteArea/finiteArea/gradSchemes/leastSquaresFaGrad/leastSquaresFaVectors.C
index f2bd352bbd..e40618b0a0 100644
--- a/src/finiteArea/finiteArea/gradSchemes/leastSquaresFaGrad/leastSquaresFaVectors.C
+++ b/src/finiteArea/finiteArea/gradSchemes/leastSquaresFaGrad/leastSquaresFaVectors.C
@@ -148,26 +148,8 @@ void Foam::leastSquaresFaVectors::makeLeastSquaresVectors() const
     }
 
 
-    // Invert the dd tensor.
-
-    // Cannot rely on the usual field inv() since that only uses the
-    // first element to guess if the remaining tensors are 2D (or
-    // singular). We, however, can have a mixture (eg, skipping over
-    // zero-length edges can yield a zero). Instead use the
-    // 'failsafe' inv() that checks each tensor (#2724)
-
-    // Fragile:  const symmTensorField invDd(inv(dd));
-
-    symmTensorField invDd(dd.size());
-    {
-        const label loopLen = dd.size();
-
-        /* pragmas... */
-        for (label i = 0; i < loopLen; ++i)
-        {
-            invDd[i] = dd[i].inv(true);  // With 'failsafe' handling
-        }
-    }
+    // Invert the dd tensors - including failsafe checks
+    const symmTensorField invDd(inv(dd));
 
 
     // Revisit all faces and calculate the lsP and lsN vectors
diff --git a/src/finiteVolume/finiteVolume/gradSchemes/leastSquaresGrad/invDistLeastSquaresVectors.C b/src/finiteVolume/finiteVolume/gradSchemes/leastSquaresGrad/invDistLeastSquaresVectors.C
index 5bfe9a515f..584968db7d 100644
--- a/src/finiteVolume/finiteVolume/gradSchemes/leastSquaresGrad/invDistLeastSquaresVectors.C
+++ b/src/finiteVolume/finiteVolume/gradSchemes/leastSquaresGrad/invDistLeastSquaresVectors.C
@@ -104,14 +104,17 @@ void Foam::leastSquaresVectors::calcLeastSquaresVectors()
         const label nei = neighbour[facei];
 
         const vector d(C[nei] - C[own]);
-        const symmTensor wdd(sqr(d)/magSqr(d));
-        dd[own] += wdd;
-        dd[nei] += wdd;
+        const scalar magSqrDist = d.magSqr();
+
+        if (magSqrDist > ROOTVSMALL)
+        {
+            const symmTensor wdd(sqr(d)/magSqrDist);
+            dd[own] += wdd;
+            dd[nei] += wdd;
+        }
     }
 
-
-    surfaceVectorField::Boundary& blsP =
-        pVectors_.boundaryField();
+    auto& blsP = pVectors_.boundaryField();
 
     forAll(blsP, patchi)
     {
@@ -126,13 +129,17 @@ void Foam::leastSquaresVectors::calcLeastSquaresVectors()
         forAll(pd, patchFacei)
         {
             const vector& d = pd[patchFacei];
+            const scalar magSqrDist = d.magSqr();
 
-            dd[faceCells[patchFacei]] += sqr(d)/magSqr(d);
+            if (magSqrDist > ROOTVSMALL)
+            {
+                dd[faceCells[patchFacei]] += sqr(d)/magSqrDist;
+            }
         }
     }
 
 
-    // Invert the dd tensor
+    // Invert the dd tensors - including failsafe checks
     const symmTensorField invDd(inv(dd));
 
 
@@ -143,9 +150,18 @@ void Foam::leastSquaresVectors::calcLeastSquaresVectors()
         const label nei = neighbour[facei];
 
         const vector d(C[nei] - C[own]);
+        const scalar magSqrDist = d.magSqr();
 
-        pVectors_[facei] = (invDd[own] & d)/magSqr(d);
-        nVectors_[facei] = -(invDd[nei] & d)/magSqr(d);
+        if (magSqrDist > ROOTVSMALL)
+        {
+            pVectors_[facei] = (invDd[own] & d)/magSqrDist;
+            nVectors_[facei] = -(invDd[nei] & d)/magSqrDist;
+        }
+        else
+        {
+            pVectors_[facei] = Zero;
+            nVectors_[facei] = Zero;
+        }
     }
 
     forAll(blsP, patchi)
@@ -161,8 +177,17 @@ void Foam::leastSquaresVectors::calcLeastSquaresVectors()
         forAll(pd, patchFacei)
         {
             const vector& d = pd[patchFacei];
+            const scalar magSqrDist = d.magSqr();
 
-            patchLsP[patchFacei] = (invDd[faceCells[patchFacei]] & d)/magSqr(d);
+            if (magSqrDist > ROOTVSMALL)
+            {
+                patchLsP[patchFacei] =
+                    (invDd[faceCells[patchFacei]] & d)/magSqrDist;
+            }
+            else
+            {
+                patchLsP[patchFacei] = Zero;
+            }
         }
     }
 
diff --git a/src/finiteVolume/finiteVolume/gradSchemes/leastSquaresGrad/leastSquaresVectors.C b/src/finiteVolume/finiteVolume/gradSchemes/leastSquaresGrad/leastSquaresVectors.C
index 40dfc42445..c8f5b01051 100644
--- a/src/finiteVolume/finiteVolume/gradSchemes/leastSquaresGrad/leastSquaresVectors.C
+++ b/src/finiteVolume/finiteVolume/gradSchemes/leastSquaresGrad/leastSquaresVectors.C
@@ -151,7 +151,7 @@ void Foam::leastSquaresVectors::calcLeastSquaresVectors()
     }
 
 
-    // Invert the dd tensor
+    // Invert the dd tensors - including failsafe checks
     const symmTensorField invDd(inv(dd));
 
 
diff --git a/src/finiteVolume/finiteVolume/gradSchemes/leastSquaresGrad/unweightedLeastSquaresVectors.C b/src/finiteVolume/finiteVolume/gradSchemes/leastSquaresGrad/unweightedLeastSquaresVectors.C
index 20c8bf5406..c19c1ba86b 100644
--- a/src/finiteVolume/finiteVolume/gradSchemes/leastSquaresGrad/unweightedLeastSquaresVectors.C
+++ b/src/finiteVolume/finiteVolume/gradSchemes/leastSquaresGrad/unweightedLeastSquaresVectors.C
@@ -129,7 +129,7 @@ void Foam::leastSquaresVectors::calcLeastSquaresVectors()
     }
 
 
-    // Invert the dd tensor
+    // Invert the dd tensors - including failsafe checks
     const symmTensorField invDd(inv(dd));