diff --git a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/backgroundMeshDecomposition/backgroundMeshDecomposition.C b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/backgroundMeshDecomposition/backgroundMeshDecomposition.C
index 7889a6ea3..c55a00332 100644
--- a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/backgroundMeshDecomposition/backgroundMeshDecomposition.C
+++ b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/backgroundMeshDecomposition/backgroundMeshDecomposition.C
@@ -692,8 +692,6 @@ void Foam::backgroundMeshDecomposition::buildPatchAndTree()
     // Overall bb
     treeBoundBox overallBb(boundaryFacesPtr_().localPoints());
 
-    Random& rnd = rndGen_;
-
     bFTreePtr_.reset
     (
         new indexedOctree<treeDataBPatch>
@@ -704,7 +702,7 @@ void Foam::backgroundMeshDecomposition::buildPatchAndTree()
                 boundaryFacesPtr_(),
                 indexedOctree<treeDataBPatch>::perturbTol()
             ),
-            overallBb.extend(rnd, 1e-4),
+            overallBb.extend(1e-4),
             10, // maxLevel
             10, // leafSize
             3.0 // duplicity
diff --git a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformalVoronoiMesh/conformalVoronoiMeshConformToSurface.C b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformalVoronoiMesh/conformalVoronoiMeshConformToSurface.C
index 4036f750a..ba0f5ed19 100644
--- a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformalVoronoiMesh/conformalVoronoiMeshConformToSurface.C
+++ b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformalVoronoiMesh/conformalVoronoiMeshConformToSurface.C
@@ -1978,12 +1978,9 @@ void Foam::conformalVoronoiMesh::buildEdgeLocationTree
 {
     treeBoundBox overallBb
     (
-        geometryToConformTo_.globalBounds().extend(rndGen_, 1e-4)
+        geometryToConformTo_.globalBounds().extend(1e-4)
     );
 
-    overallBb.min() -= Foam::point(rootVSmall, rootVSmall, rootVSmall);
-    overallBb.max() += Foam::point(rootVSmall, rootVSmall, rootVSmall);
-
     edgeLocationTreePtr_.reset
     (
         new dynamicIndexedOctree<dynamicTreeDataPoint>
@@ -2005,12 +2002,9 @@ void Foam::conformalVoronoiMesh::buildSurfacePtLocationTree
 {
     treeBoundBox overallBb
     (
-        geometryToConformTo_.globalBounds().extend(rndGen_, 1e-4)
+        geometryToConformTo_.globalBounds().extend(1e-4)
     );
 
-    overallBb.min() -= Foam::point(rootVSmall, rootVSmall, rootVSmall);
-    overallBb.max() += Foam::point(rootVSmall, rootVSmall, rootVSmall);
-
     surfacePtLocationTreePtr_.reset
     (
         new dynamicIndexedOctree<dynamicTreeDataPoint>
diff --git a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformationSurfaces/conformationSurfaces.C b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformationSurfaces/conformationSurfaces.C
index 7f5b8e7a0..5de4b45de 100644
--- a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformationSurfaces/conformationSurfaces.C
+++ b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformationSurfaces/conformationSurfaces.C
@@ -558,10 +558,7 @@ Foam::conformationSurfaces::conformationSurfaces
 
     // Extend the global bounds to stop the bound box sitting on the surfaces
     // to be conformed to
-    // globalBounds_ = globalBounds_.extend(rndGen_, 1e-4);
-
     vector newSpan = 1e-4*globalBounds_.span();
-
     globalBounds_.min() -= newSpan;
     globalBounds_.max() += newSpan;
 
diff --git a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/initialPointsMethod/autoDensity/autoDensity.C b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/initialPointsMethod/autoDensity/autoDensity.C
index c41a8568e..b7e2a03db 100644
--- a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/initialPointsMethod/autoDensity/autoDensity.C
+++ b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/initialPointsMethod/autoDensity/autoDensity.C
@@ -919,11 +919,7 @@ List<Vb::Point> autoDensity::initialPoints() const
     else
     {
         // Extend the global box to move it off large plane surfaces
-        hierBB = geometryToConformTo().globalBounds().extend
-        (
-            rndGen(),
-            1e-6
-        );
+        hierBB = geometryToConformTo().globalBounds().extend(1e-6);
     }
 
     DynamicList<Vb::Point> initialPoints;
diff --git a/applications/utilities/preProcessing/viewFactorsGen/searchingEngine.H b/applications/utilities/preProcessing/viewFactorsGen/searchingEngine.H
index 3711aff9b..4518cfc32 100644
--- a/applications/utilities/preProcessing/viewFactorsGen/searchingEngine.H
+++ b/applications/utilities/preProcessing/viewFactorsGen/searchingEngine.H
@@ -7,7 +7,7 @@ List<treeBoundBox> meshBb
     treeBoundBox
     (
         boundBox(coarseMesh.points(), false)
-    ).extend(rndGen, 1e-3)
+    ).extend(1e-3)
 );
 
 // Dummy bounds dictionary
diff --git a/applications/utilities/surface/surfaceHookUp/surfaceHookUp.C b/applications/utilities/surface/surfaceHookUp/surfaceHookUp.C
index a376bf65c..074faecda 100644
--- a/applications/utilities/surface/surfaceHookUp/surfaceHookUp.C
+++ b/applications/utilities/surface/surfaceHookUp/surfaceHookUp.C
@@ -174,12 +174,9 @@ void createBoundaryEdgeTrees
         // geometry there are less face/edge aligned items.
         treeBoundBox bb
         (
-            treeBoundBox(UList<point>(surf.localPoints())).extend(rndGen, 1e-4)
+            treeBoundBox(UList<point>(surf.localPoints())).extend(1e-4)
         );
 
-        bb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-        bb.max() += point(rootVSmall, rootVSmall, rootVSmall);
-
         bEdgeTrees.set
         (
             surfI,
diff --git a/applications/utilities/surface/surfaceRedistributePar/surfaceRedistributePar.C b/applications/utilities/surface/surfaceRedistributePar/surfaceRedistributePar.C
index e825a1397..ee419d0bc 100644
--- a/applications/utilities/surface/surfaceRedistributePar/surfaceRedistributePar.C
+++ b/applications/utilities/surface/surfaceRedistributePar/surfaceRedistributePar.C
@@ -144,18 +144,13 @@ int main(int argc, char *argv[])
 
     #include "createPolyMesh.H"
 
-    Random rndGen(653213);
-
     // Determine mesh bounding boxes:
     List<List<treeBoundBox>> meshBb(Pstream::nProcs());
     {
         meshBb[Pstream::myProcNo()] = List<treeBoundBox>
         (
             1,
-            treeBoundBox
-            (
-                boundBox(mesh.points(), false)
-            ).extend(rndGen, 1e-3)
+            treeBoundBox(boundBox(mesh.points(), false)).extend(1e-3)
         );
         Pstream::gatherList(meshBb);
         Pstream::scatterList(meshBb);
diff --git a/src/OpenFOAM/meshes/polyMesh/polyMesh.C b/src/OpenFOAM/meshes/polyMesh/polyMesh.C
index c9a0011d4..5aca1df36 100644
--- a/src/OpenFOAM/meshes/polyMesh/polyMesh.C
+++ b/src/OpenFOAM/meshes/polyMesh/polyMesh.C
@@ -876,14 +876,6 @@ Foam::polyMesh::cellTree() const
 {
     if (cellTreePtr_.empty())
     {
-        treeBoundBox overallBb(points());
-
-        static Random rndGen(261782);
-
-        overallBb = overallBb.extend(rndGen, 1e-4);
-        overallBb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-        overallBb.max() += point(rootVSmall, rootVSmall, rootVSmall);
-
         cellTreePtr_.reset
         (
             new indexedOctree<treeDataCell>
@@ -894,7 +886,7 @@ Foam::polyMesh::cellTree() const
                     *this,
                     CELL_TETS   // use tet-decomposition for any inside test
                 ),
-                overallBb,
+                treeBoundBox(points()).extend(1e-4),
                 8,              // maxLevel
                 10,             // leafsize
                 5.0             // duplicity
diff --git a/src/OpenFOAM/meshes/treeBoundBox/treeBoundBox.H b/src/OpenFOAM/meshes/treeBoundBox/treeBoundBox.H
index 8c35577fd..3dcf163ff 100644
--- a/src/OpenFOAM/meshes/treeBoundBox/treeBoundBox.H
+++ b/src/OpenFOAM/meshes/treeBoundBox/treeBoundBox.H
@@ -344,10 +344,9 @@ public:
             //   0 : none of the above.
             label distanceCmp(const point&, const treeBoundBox& other) const;
 
-            //- Return slightly wider bounding box
-            //  Extends all dimensions with s*span*Random::scalar01()
-            //  and guarantees in any direction s*mag(span) minimum width
-            inline treeBoundBox extend(Random&, const scalar s) const;
+            //- Return asymetrically extended bounding box, with guaranteed
+            //  minimum width of s*mag(span) in any direction
+            inline treeBoundBox extend(const scalar s) const;
 
     // Write
 
diff --git a/src/OpenFOAM/meshes/treeBoundBox/treeBoundBoxI.H b/src/OpenFOAM/meshes/treeBoundBox/treeBoundBoxI.H
index 3480eac00..a4c24794c 100644
--- a/src/OpenFOAM/meshes/treeBoundBox/treeBoundBoxI.H
+++ b/src/OpenFOAM/meshes/treeBoundBox/treeBoundBoxI.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     |
-    \\  /    A nd           | Copyright (C) 2011 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2018 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -312,27 +312,18 @@ inline void Foam::treeBoundBox::searchOrder
 }
 
 
-//- Return slightly wider bounding box
-inline Foam::treeBoundBox Foam::treeBoundBox::extend
-(
-    Random& rndGen,
-    const scalar s
-) const
+inline Foam::treeBoundBox Foam::treeBoundBox::extend(const scalar s) const
 {
+    // Numbers that don't approximate rational fractions with which to make the
+    // box asymmetric. These are between one and two.
+    static const vector a = vector::uniform(sqrt(1.25) + 0.5);
+    static const vector b = vector::uniform(sqrt(2.0));
+
     treeBoundBox bb(*this);
 
-    vector newSpan = bb.span();
-
-    // Make 3D
-    scalar minSpan = s * Foam::mag(newSpan);
-
-    for (direction dir = 0; dir < vector::nComponents; dir++)
-    {
-        newSpan[dir] = Foam::max(newSpan[dir], minSpan);
-    }
-
-    bb.min() -= cmptMultiply(s * rndGen.vector01(), newSpan);
-    bb.max() += cmptMultiply(s * rndGen.vector01(), newSpan);
+    const scalar delta = s*Foam::mag(bb.span());
+    bb.min() -= Foam::max(delta*a, vector::uniform(rootVSmall));
+    bb.max() += Foam::max(delta*b, vector::uniform(rootVSmall));
 
     return bb;
 }
diff --git a/src/dynamicMesh/polyMeshAdder/faceCoupleInfo.C b/src/dynamicMesh/polyMeshAdder/faceCoupleInfo.C
index 57f7d25f8..b67eb1297 100644
--- a/src/dynamicMesh/polyMeshAdder/faceCoupleInfo.C
+++ b/src/dynamicMesh/polyMeshAdder/faceCoupleInfo.C
@@ -980,8 +980,6 @@ void Foam::faceCoupleInfo::findSlavesCoveringMaster
 
     treeBoundBox overallBb(mesh0.points());
 
-    Random rndGen(123456);
-
     indexedOctree<treeDataFace> tree
     (
         treeDataFace    // all information needed to search faces
@@ -990,7 +988,7 @@ void Foam::faceCoupleInfo::findSlavesCoveringMaster
             mesh0,
             bndFaces                    // boundary faces only
         ),
-        overallBb.extend(rndGen, 1e-4), // overall search domain
+        overallBb.extend(1e-4),         // overall search domain
         8,                              // maxLevel
         10,                             // leafsize
         3.0                             // duplicity
diff --git a/src/lagrangian/basic/InteractionLists/InteractionLists.C b/src/lagrangian/basic/InteractionLists/InteractionLists.C
index b223232bd..f5bd5fd87 100644
--- a/src/lagrangian/basic/InteractionLists/InteractionLists.C
+++ b/src/lagrangian/basic/InteractionLists/InteractionLists.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     |
-    \\  /    A nd           | Copyright (C) 2011-2017 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2018 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -39,8 +39,6 @@ void Foam::InteractionLists<ParticleType>::buildInteractionLists()
     Info<< "Building InteractionLists with interaction distance "
         << maxDistance_ << endl;
 
-    Random rndGen(419715);
-
     const vector interactionVec = maxDistance_*vector::one;
 
     treeBoundBox procBb(treeBoundBox(mesh_.points()));
@@ -158,7 +156,7 @@ void Foam::InteractionLists<ParticleType>::buildInteractionLists()
 
     treeBoundBox procBbRndExt
     (
-        treeBoundBox(mesh_.points()).extend(rndGen, 1e-4)
+        treeBoundBox(mesh_.points()).extend(1e-4)
     );
 
     indexedOctree<treeDataCell> coupledPatchRangeTree
diff --git a/src/mesh/snappyHexMesh/meshRefinement/meshRefinement.C b/src/mesh/snappyHexMesh/meshRefinement/meshRefinement.C
index 887ce8dd8..752da9f25 100644
--- a/src/mesh/snappyHexMesh/meshRefinement/meshRefinement.C
+++ b/src/mesh/snappyHexMesh/meshRefinement/meshRefinement.C
@@ -2402,13 +2402,10 @@ void Foam::meshRefinement::distribute(const mapDistributePolyMesh& map)
 
     // Redistribute surface and any fields on it.
     {
-        Random rndGen(653213);
-
         // Get local mesh bounding box. Single box for now.
         List<treeBoundBox> meshBb(1);
         treeBoundBox& bb = meshBb[0];
-        bb = treeBoundBox(mesh_.points());
-        bb = bb.extend(rndGen, 1e-4);
+        bb = treeBoundBox(mesh_.points()).extend(1e-4);
 
         // Distribute all geometry (so refinementSurfaces and shellSurfaces)
         searchableSurfaces& geometry =
diff --git a/src/mesh/snappyHexMesh/refinementFeatures/refinementFeatures.C b/src/mesh/snappyHexMesh/refinementFeatures/refinementFeatures.C
index d8bb33a50..e9091dc68 100644
--- a/src/mesh/snappyHexMesh/refinementFeatures/refinementFeatures.C
+++ b/src/mesh/snappyHexMesh/refinementFeatures/refinementFeatures.C
@@ -253,14 +253,9 @@ void Foam::refinementFeatures::buildTrees(const label featI)
     // Calculate bb of all points
     treeBoundBox bb(points);
 
-    // Random number generator. Bit dodgy since not exactly random ;-)
-    Random rndGen(65431);
-
     // Slightly extended bb. Slightly off-centred just so on symmetric
     // geometry there are less face/edge aligned items.
-    bb = bb.extend(rndGen, 1e-4);
-    bb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-    bb.max() += point(rootVSmall, rootVSmall, rootVSmall);
+    bb = bb.extend(1e-4);
 
     edgeTrees_.set
     (
@@ -394,14 +389,9 @@ Foam::refinementFeatures::regionEdgeTrees() const
             // Calculate bb of all points
             treeBoundBox bb(points);
 
-            // Random number generator. Bit dodgy since not exactly random ;-)
-            Random rndGen(65431);
-
             // Slightly extended bb. Slightly off-centred just so on symmetric
             // geometry there are less face/edge aligned items.
-            bb = bb.extend(rndGen, 1e-4);
-            bb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-            bb.max() += point(rootVSmall, rootVSmall, rootVSmall);
+            bb = bb.extend(1e-4);
 
             trees.set
             (
diff --git a/src/mesh/snappyHexMesh/snappyHexMeshDriver/snappySnapDriverFeature.C b/src/mesh/snappyHexMesh/snappyHexMeshDriver/snappySnapDriverFeature.C
index 8f7adad32..648253c86 100644
--- a/src/mesh/snappyHexMesh/snappyHexMeshDriver/snappySnapDriverFeature.C
+++ b/src/mesh/snappyHexMesh/snappyHexMeshDriver/snappySnapDriverFeature.C
@@ -2466,16 +2466,7 @@ void Foam::snappySnapDriver::reverseAttractMeshPoints
 
     // Get search domain and extend it a bit
     treeBoundBox bb(pp.localPoints());
-    {
-        // Random number generator. Bit dodgy since not exactly random ;-)
-        Random rndGen(65431);
-
-        // Slightly extended bb. Slightly off-centred just so on symmetric
-        // geometry there are less face/edge aligned items.
-        bb = bb.extend(rndGen, 1e-4);
-        bb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-        bb.max() += point(rootVSmall, rootVSmall, rootVSmall);
-    }
+    bb = bb.extend(1e-4);
 
     // Collect candidate points for attraction
     DynamicList<label> attractPoints(pp.nPoints());
diff --git a/src/meshTools/edgeMesh/extendedEdgeMesh/extendedEdgeMesh.C b/src/meshTools/edgeMesh/extendedEdgeMesh/extendedEdgeMesh.C
index be8164f87..d4eca1964 100644
--- a/src/meshTools/edgeMesh/extendedEdgeMesh/extendedEdgeMesh.C
+++ b/src/meshTools/edgeMesh/extendedEdgeMesh/extendedEdgeMesh.C
@@ -826,17 +826,9 @@ Foam::extendedEdgeMesh::pointTree() const
 {
     if (pointTree_.empty())
     {
-        Random rndGen(17301893);
-
         // Slightly extended bb. Slightly off-centred just so on symmetric
         // geometry there are less face/edge aligned items.
-        treeBoundBox bb
-        (
-            treeBoundBox(points()).extend(rndGen, 1e-4)
-        );
-
-        bb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-        bb.max() += point(rootVSmall, rootVSmall, rootVSmall);
+        treeBoundBox bb(treeBoundBox(points()).extend(1e-4));
 
         const labelList featurePointLabels = identity(nonFeatureStart_);
 
@@ -866,17 +858,9 @@ Foam::extendedEdgeMesh::edgeTree() const
 {
     if (edgeTree_.empty())
     {
-        Random rndGen(17301893);
-
         // Slightly extended bb. Slightly off-centred just so on symmetric
         // geometry there are less face/edge aligned items.
-        treeBoundBox bb
-        (
-            treeBoundBox(points()).extend(rndGen, 1e-4)
-        );
-
-        bb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-        bb.max() += point(rootVSmall, rootVSmall, rootVSmall);
+        treeBoundBox bb(treeBoundBox(points()).extend(1e-4));
 
         labelList allEdges(identity(edges().size()));
 
@@ -910,17 +894,9 @@ Foam::extendedEdgeMesh::edgeTreesByType() const
     {
         edgeTreesByType_.setSize(nEdgeTypes);
 
-        Random rndGen(872141);
-
         // Slightly extended bb. Slightly off-centred just so on symmetric
         // geometry there are less face/edge aligned items.
-        treeBoundBox bb
-        (
-            treeBoundBox(points()).extend(rndGen, 1e-4)
-        );
-
-        bb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-        bb.max() += point(rootVSmall, rootVSmall, rootVSmall);
+        treeBoundBox bb(treeBoundBox(points()).extend(1e-4));
 
         labelListList sliceEdges(nEdgeTypes);
 
diff --git a/src/meshTools/mappedPatches/mappedPolyPatch/mappedPatchBase.C b/src/meshTools/mappedPatches/mappedPolyPatch/mappedPatchBase.C
index 61dff7c55..03cc0cfde 100644
--- a/src/meshTools/mappedPatches/mappedPolyPatch/mappedPatchBase.C
+++ b/src/meshTools/mappedPatches/mappedPolyPatch/mappedPatchBase.C
@@ -273,8 +273,6 @@ void Foam::mappedPatchBase::findSamples
 
         case NEARESTPATCHFACE:
         {
-            Random rndGen(123456);
-
             const polyPatch& pp = samplePolyPatch();
 
             if (pp.empty())
@@ -292,14 +290,8 @@ void Foam::mappedPatchBase::findSamples
 
                 treeBoundBox patchBb
                 (
-                    treeBoundBox(pp.points(), pp.meshPoints()).extend
-                    (
-                        rndGen,
-                        1e-4
-                    )
+                    treeBoundBox(pp.points(), pp.meshPoints()).extend(1e-4)
                 );
-                patchBb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-                patchBb.max() += point(rootVSmall, rootVSmall, rootVSmall);
 
                 indexedOctree<treeDataFace> boundaryTree
                 (
@@ -347,8 +339,6 @@ void Foam::mappedPatchBase::findSamples
 
         case NEARESTPATCHPOINT:
         {
-            Random rndGen(123456);
-
             const polyPatch& pp = samplePolyPatch();
 
             if (pp.empty())
@@ -364,14 +354,8 @@ void Foam::mappedPatchBase::findSamples
                 // patch (local) points
                 treeBoundBox patchBb
                 (
-                    treeBoundBox(pp.points(), pp.meshPoints()).extend
-                    (
-                        rndGen,
-                        1e-4
-                    )
+                    treeBoundBox(pp.points(), pp.meshPoints()).extend(1e-4)
                 );
-                patchBb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-                patchBb.max() += point(rootVSmall, rootVSmall, rootVSmall);
 
                 indexedOctree<treeDataPoint> boundaryTree
                 (
diff --git a/src/meshTools/meshSearch/meshSearch.C b/src/meshTools/meshSearch/meshSearch.C
index 37a6af631..a15b644ab 100644
--- a/src/meshTools/meshSearch/meshSearch.C
+++ b/src/meshTools/meshSearch/meshSearch.C
@@ -552,17 +552,15 @@ Foam::meshSearch::boundaryTree() const
 
         if (!overallBbPtr_.valid())
         {
-            Random rndGen(261782);
             overallBbPtr_.reset
             (
                 new treeBoundBox(mesh_.points())
             );
 
             treeBoundBox& overallBb = overallBbPtr_();
+
             // Extend slightly and make 3D
-            overallBb = overallBb.extend(rndGen, 1e-4);
-            overallBb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-            overallBb.max() += point(rootVSmall, rootVSmall, rootVSmall);
+            overallBb = overallBb.extend(1e-4);
         }
 
         // all boundary faces (not just walls)
@@ -605,17 +603,15 @@ Foam::meshSearch::cellTree() const
 
         if (!overallBbPtr_.valid())
         {
-            Random rndGen(261782);
             overallBbPtr_.reset
             (
                 new treeBoundBox(mesh_.points())
             );
 
             treeBoundBox& overallBb = overallBbPtr_();
+
             // Extend slightly and make 3D
-            overallBb = overallBb.extend(rndGen, 1e-4);
-            overallBb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-            overallBb.max() += point(rootVSmall, rootVSmall, rootVSmall);
+            overallBb = overallBb.extend(1e-4);
         }
 
         cellTreePtr_.reset
diff --git a/src/meshTools/searchableSurfaces/triSurfaceMesh/triSurfaceMesh.C b/src/meshTools/searchableSurfaces/triSurfaceMesh/triSurfaceMesh.C
index fa89b1c05..47aa0a231 100644
--- a/src/meshTools/searchableSurfaces/triSurfaceMesh/triSurfaceMesh.C
+++ b/src/meshTools/searchableSurfaces/triSurfaceMesh/triSurfaceMesh.C
@@ -565,15 +565,9 @@ Foam::triSurfaceMesh::edgeTree() const
                 nPoints
             );
 
-            // Random number generator. Bit dodgy since not exactly random ;-)
-            Random rndGen(65431);
-
             // Slightly extended bb. Slightly off-centred just so on symmetric
             // geometry there are less face/edge aligned items.
-
-            bb = bb.extend(rndGen, 1e-4);
-            bb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-            bb.max() += point(rootVSmall, rootVSmall, rootVSmall);
+            bb = bb.extend(1e-4);
         }
 
         scalar oldTol = indexedOctree<treeDataEdge>::perturbTol();
diff --git a/src/meshTools/triSurface/triSurfaceSearch/triSurfaceRegionSearch.C b/src/meshTools/triSurface/triSurfaceSearch/triSurfaceRegionSearch.C
index b053515f0..414357337 100644
--- a/src/meshTools/triSurface/triSurfaceSearch/triSurfaceRegionSearch.C
+++ b/src/meshTools/triSurface/triSurfaceSearch/triSurfaceRegionSearch.C
@@ -144,16 +144,10 @@ Foam::triSurfaceRegionSearch::treeByRegion() const
     //                    << endl;
     //            }
 
-                // Random number generator. Bit dodgy since not exactly
-                // random ;-)
-                Random rndGen(65431);
-
                 // Slightly extended bb. Slightly off-centred just so
                 // on symmetric geometry there are fewer face/edge
                 // aligned items.
-                bb = bb.extend(rndGen, 1e-4);
-                bb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-                bb.max() += point(rootVSmall, rootVSmall, rootVSmall);
+                bb = bb.extend(1e-4);
             }
 
             treeByRegion_.set
diff --git a/src/meshTools/triSurface/triSurfaceSearch/triSurfaceSearch.C b/src/meshTools/triSurface/triSurfaceSearch/triSurfaceSearch.C
index 410b24829..cb924f515 100644
--- a/src/meshTools/triSurface/triSurfaceSearch/triSurfaceSearch.C
+++ b/src/meshTools/triSurface/triSurfaceSearch/triSurfaceSearch.C
@@ -217,14 +217,9 @@ Foam::triSurfaceSearch::tree() const
                     << endl;
             }
 
-            // Random number generator. Bit dodgy since not exactly random ;-)
-            Random rndGen(65431);
-
             // Slightly extended bb. Slightly off-centred just so on symmetric
             // geometry there are less face/edge aligned items.
-            bb = bb.extend(rndGen, 1e-4);
-            bb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-            bb.max() += point(rootVSmall, rootVSmall, rootVSmall);
+            bb = bb.extend(1e-4);
         }
 
         scalar oldTol = indexedOctree<treeDataTriSurface>::perturbTol();
diff --git a/src/sampling/probes/patchProbes.C b/src/sampling/probes/patchProbes.C
index 4eaf2c209..5fb0e9cda 100644
--- a/src/sampling/probes/patchProbes.C
+++ b/src/sampling/probes/patchProbes.C
@@ -78,10 +78,7 @@ void Foam::patchProbes::findElements(const fvMesh& mesh)
         }
 
         treeBoundBox overallBb(pp.points());
-        Random rndGen(123456);
-        overallBb = overallBb.extend(rndGen, 1e-4);
-        overallBb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-        overallBb.max() += point(rootVSmall, rootVSmall, rootVSmall);
+        overallBb = overallBb.extend(1e-4);
 
         const indexedOctree<treeDataFace> boundaryTree
         (
diff --git a/src/sampling/sampledSet/patchCloud/patchCloudSet.C b/src/sampling/sampledSet/patchCloud/patchCloudSet.C
index ef42db571..8bbe49cb4 100644
--- a/src/sampling/sampledSet/patchCloud/patchCloudSet.C
+++ b/src/sampling/sampledSet/patchCloud/patchCloudSet.C
@@ -90,16 +90,7 @@ void Foam::patchCloudSet::calcSamples
         bb.min() = min(bb.min(), patchBb.min());
         bb.max() = max(bb.max(), patchBb.max());
     }
-
-    // Not very random
-    Random rndGen(123456);
-    // Make bb asymetric just to avoid problems on symmetric meshes
-    bb = bb.extend(rndGen, 1e-4);
-
-    // Make sure bb is 3D.
-    bb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-    bb.max() += point(rootVSmall, rootVSmall, rootVSmall);
-
+    bb = bb.extend(1e-4);
 
     indexedOctree<treeDataFace> patchTree
     (
diff --git a/src/sampling/sampledSurface/sampledTriSurfaceMesh/sampledTriSurfaceMesh.C b/src/sampling/sampledSurface/sampledTriSurfaceMesh/sampledTriSurfaceMesh.C
index e74a72845..cc90660f8 100644
--- a/src/sampling/sampledSurface/sampledTriSurfaceMesh/sampledTriSurfaceMesh.C
+++ b/src/sampling/sampledSurface/sampledTriSurfaceMesh/sampledTriSurfaceMesh.C
@@ -109,10 +109,7 @@ Foam::sampledTriSurfaceMesh::nonCoupledboundaryTree() const
 
 
         treeBoundBox overallBb(mesh().points());
-        Random rndGen(123456);
-        overallBb = overallBb.extend(rndGen, 1e-4);
-        overallBb.min() -= point(rootVSmall, rootVSmall, rootVSmall);
-        overallBb.max() += point(rootVSmall, rootVSmall, rootVSmall);
+        overallBb = overallBb.extend(1e-4);
 
         boundaryTreePtr_.reset
         (