diff --git a/applications/utilities/mesh/manipulation/checkMesh/checkGeometry.C b/applications/utilities/mesh/manipulation/checkMesh/checkGeometry.C
index 8677f08c6..987e26d2e 100644
--- a/applications/utilities/mesh/manipulation/checkMesh/checkGeometry.C
+++ b/applications/utilities/mesh/manipulation/checkMesh/checkGeometry.C
@@ -136,7 +136,7 @@ bool Foam::checkWedges
                 const point& pt = p[pp.meshPoints()[i]];
                 scalar d = mag((pt - p0) & pp.n());
 
-                if (d > sqrt(SMALL))
+                if (d > ROOTSMALL)
                 {
                     if (report)
                     {
diff --git a/src/OpenFOAM/primitives/Scalar/doubleScalar/doubleScalar.H b/src/OpenFOAM/primitives/Scalar/doubleScalar/doubleScalar.H
index 2498f5f9c..308994785 100644
--- a/src/OpenFOAM/primitives/Scalar/doubleScalar/doubleScalar.H
+++ b/src/OpenFOAM/primitives/Scalar/doubleScalar/doubleScalar.H
@@ -55,6 +55,7 @@ static const doubleScalar doubleScalarGREAT = 1.0e+15;
 static const doubleScalar doubleScalarVGREAT = 1.0e+300;
 static const doubleScalar doubleScalarROOTVGREAT = 1.0e+150;
 static const doubleScalar doubleScalarSMALL = 1.0e-15;
+static const doubleScalar doubleScalarROOTSMALL = 3.0e-8;
 static const doubleScalar doubleScalarVSMALL = 1.0e-300;
 static const doubleScalar doubleScalarROOTVSMALL = 1.0e-150;
 
diff --git a/src/OpenFOAM/primitives/Scalar/floatScalar/floatScalar.H b/src/OpenFOAM/primitives/Scalar/floatScalar/floatScalar.H
index 31ae9891d..1cfb728a2 100644
--- a/src/OpenFOAM/primitives/Scalar/floatScalar/floatScalar.H
+++ b/src/OpenFOAM/primitives/Scalar/floatScalar/floatScalar.H
@@ -55,6 +55,7 @@ static const floatScalar floatScalarGREAT = 1.0e+6;
 static const floatScalar floatScalarVGREAT = 1.0e+37;
 static const floatScalar floatScalarROOTVGREAT = 1.0e+18;
 static const floatScalar floatScalarSMALL = 1.0e-6;
+static const floatScalar floatScalarROOTSMALL = 1.0e-3;
 static const floatScalar floatScalarVSMALL = 1.0e-37;
 static const floatScalar floatScalarROOTVSMALL = 1.0e-18;
 
diff --git a/src/OpenFOAM/primitives/Scalar/scalar/scalar.H b/src/OpenFOAM/primitives/Scalar/scalar/scalar.H
index cb5496a65..8f9c1c561 100644
--- a/src/OpenFOAM/primitives/Scalar/scalar/scalar.H
+++ b/src/OpenFOAM/primitives/Scalar/scalar/scalar.H
@@ -53,6 +53,7 @@ namespace Foam
     static const scalar VGREAT = floatScalarVGREAT;
     static const scalar ROOTVGREAT = floatScalarROOTVGREAT;
     static const scalar SMALL = floatScalarSMALL;
+    static const scalar ROOTSMALL = floatScalarROOTSMALL;
     static const scalar VSMALL = floatScalarVSMALL;
     static const scalar ROOTVSMALL = floatScalarROOTVSMALL;
 
@@ -71,6 +72,7 @@ namespace Foam
     static const scalar VGREAT = doubleScalarVGREAT;
     static const scalar ROOTVGREAT = doubleScalarROOTVGREAT;
     static const scalar SMALL = doubleScalarSMALL;
+    static const scalar ROOTSMALL = doubleScalarROOTSMALL;
     static const scalar VSMALL = doubleScalarVSMALL;
     static const scalar ROOTVSMALL = doubleScalarROOTVSMALL;
 
diff --git a/src/mesh/autoMesh/autoHexMesh/meshRefinement/meshRefinement.C b/src/mesh/autoMesh/autoHexMesh/meshRefinement/meshRefinement.C
index 5d96aafca..12e94465f 100644
--- a/src/mesh/autoMesh/autoHexMesh/meshRefinement/meshRefinement.C
+++ b/src/mesh/autoMesh/autoHexMesh/meshRefinement/meshRefinement.C
@@ -272,7 +272,7 @@ void Foam::meshRefinement::updateIntersections(const labelList& changedFaces)
 
     // Extend segments a bit
     {
-        const vectorField smallVec(Foam::sqrt(SMALL)*(end-start));
+        const vectorField smallVec(ROOTSMALL*(end-start));
         start -= smallVec;
         end += smallVec;
     }
@@ -483,7 +483,7 @@ void Foam::meshRefinement::checkData()
 
         // Extend segments a bit
         {
-            const vectorField smallVec(Foam::sqrt(SMALL)*(end-start));
+            const vectorField smallVec(ROOTSMALL*(end-start));
             start -= smallVec;
             end += smallVec;
         }
@@ -2897,7 +2897,7 @@ void Foam::meshRefinement::dumpIntersections(const fileName& prefix) const
 
         // Extend segments a bit
         {
-            const vectorField smallVec(Foam::sqrt(SMALL)*(end-start));
+            const vectorField smallVec(ROOTSMALL*(end-start));
             start -= smallVec;
             end += smallVec;
         }
diff --git a/src/mesh/autoMesh/autoHexMesh/meshRefinement/meshRefinementBaffles.C b/src/mesh/autoMesh/autoHexMesh/meshRefinement/meshRefinementBaffles.C
index 8cf215729..bbbe08c35 100644
--- a/src/mesh/autoMesh/autoHexMesh/meshRefinement/meshRefinementBaffles.C
+++ b/src/mesh/autoMesh/autoHexMesh/meshRefinement/meshRefinementBaffles.C
@@ -243,7 +243,7 @@ void Foam::meshRefinement::getBafflePatches
 
     // Extend segments a bit
     {
-        const vectorField smallVec(Foam::sqrt(SMALL)*(end-start));
+        const vectorField smallVec(ROOTSMALL*(end-start));
         start -= smallVec;
         end += smallVec;
     }
@@ -830,7 +830,7 @@ Foam::List<Foam::labelPair> Foam::meshRefinement::freeStandingBaffles
 
         // Extend segments a bit
         {
-            const vectorField smallVec(Foam::sqrt(SMALL)*(end-start));
+            const vectorField smallVec(ROOTSMALL*(end-start));
             start -= smallVec;
             end += smallVec;
         }
@@ -2967,7 +2967,7 @@ Foam::autoPtr<Foam::mapPolyMesh> Foam::meshRefinement::zonify
 
         // Extend segments a bit
         {
-            const vectorField smallVec(Foam::sqrt(SMALL)*(end-start));
+            const vectorField smallVec(ROOTSMALL*(end-start));
             start -= smallVec;
             end += smallVec;
         }
diff --git a/src/mesh/autoMesh/autoHexMesh/meshRefinement/meshRefinementRefine.C b/src/mesh/autoMesh/autoHexMesh/meshRefinement/meshRefinementRefine.C
index 3ccaa7283..e2224f7cd 100644
--- a/src/mesh/autoMesh/autoHexMesh/meshRefinement/meshRefinementRefine.C
+++ b/src/mesh/autoMesh/autoHexMesh/meshRefinement/meshRefinementRefine.C
@@ -967,7 +967,7 @@ Foam::label Foam::meshRefinement::markSurfaceRefinement
 
     // Extend segments a bit
     {
-        const vectorField smallVec(Foam::sqrt(SMALL)*(end-start));
+        const vectorField smallVec(ROOTSMALL*(end-start));
         start -= smallVec;
         end += smallVec;
     }
@@ -1161,7 +1161,7 @@ Foam::label Foam::meshRefinement::markSurfaceCurvatureRefinement
 
     // Extend segments a bit
     {
-        const vectorField smallVec(Foam::sqrt(SMALL)*(end-start));
+        const vectorField smallVec(ROOTSMALL*(end-start));
         start -= smallVec;
         end += smallVec;
     }
@@ -1764,7 +1764,7 @@ Foam::label Foam::meshRefinement::markProximityRefinement
 
     // Extend segments a bit
     {
-        const vectorField smallVec(Foam::sqrt(SMALL)*(end-start));
+        const vectorField smallVec(ROOTSMALL*(end-start));
         start -= smallVec;
         end += smallVec;
     }
diff --git a/src/meshTools/searchableSurface/searchableBox.C b/src/meshTools/searchableSurface/searchableBox.C
index 5970e8257..f20b808e8 100644
--- a/src/meshTools/searchableSurface/searchableBox.C
+++ b/src/meshTools/searchableSurface/searchableBox.C
@@ -531,7 +531,7 @@ void Foam::searchableBox::findLineAll
     const scalarField magSqrDirVec(magSqr(dirVec));
     const vectorField smallVec
     (
-        Foam::sqrt(SMALL)*dirVec
+        ROOTSMALL*dirVec
       + vector(ROOTVSMALL,ROOTVSMALL,ROOTVSMALL)
     );
 
diff --git a/src/parallel/distributed/distributedTriSurfaceMesh/distributedTriSurfaceMesh.C b/src/parallel/distributed/distributedTriSurfaceMesh/distributedTriSurfaceMesh.C
index 1a636b1ca..80e3943cd 100644
--- a/src/parallel/distributed/distributedTriSurfaceMesh/distributedTriSurfaceMesh.C
+++ b/src/parallel/distributed/distributedTriSurfaceMesh/distributedTriSurfaceMesh.C
@@ -1752,7 +1752,7 @@ void Foam::distributedTriSurfaceMesh::findLineAll
     const scalarField magSqrDirVec(magSqr(dirVec));
     const vectorField smallVec
     (
-        Foam::sqrt(SMALL)*dirVec
+        ROOTSMALL*dirVec
       + vector(ROOTVSMALL,ROOTVSMALL,ROOTVSMALL)
     );