diff --git a/src/BRepMesh/BRepMesh_CurveTessellator.cxx b/src/BRepMesh/BRepMesh_CurveTessellator.cxx
index e842132b12..d7e73f0f26 100644
--- a/src/BRepMesh/BRepMesh_CurveTessellator.cxx
+++ b/src/BRepMesh/BRepMesh_CurveTessellator.cxx
@@ -79,6 +79,9 @@ void BRepMesh_CurveTessellator::init()
     aPreciseLinDef *= 0.5;
   }
 
+  aPreciseLinDef = Max(aPreciseLinDef, Precision::Confusion());
+  aPreciseAngDef = Max(aPreciseAngDef, Precision::Angular());
+
   mySquareEdgeDef = aPreciseLinDef * aPreciseLinDef;
   mySquareMinSize = Max(mySquareEdgeDef, myParameters.MinSize * myParameters.MinSize);
 
diff --git a/src/GCPnts/GCPnts_TangentialDeflection.pxx b/src/GCPnts/GCPnts_TangentialDeflection.pxx
index 8d05ab02bd..068e80bac3 100644
--- a/src/GCPnts/GCPnts_TangentialDeflection.pxx
+++ b/src/GCPnts/GCPnts_TangentialDeflection.pxx
@@ -135,7 +135,9 @@ void GCPnts_TangentialDeflection::Initialize (
 
 {
   
-  Standard_ConstructionError_Raise_if (CurvatureDeflection <= Precision::Confusion () || AngularDeflection   <= Precision::Angular (), "GCPnts_TangentialDeflection::Initialize - Zero Deflection")
+  Standard_ConstructionError_Raise_if (CurvatureDeflection < Precision::Confusion () ||
+                                       AngularDeflection < Precision::Angular (),
+                                       "GCPnts_TangentialDeflection::Initialize - Zero Deflection")
 
  parameters.Clear ();
  points    .Clear ();