diff --git a/src/BOPAlgo/BOPAlgo_PaveFiller.hxx b/src/BOPAlgo/BOPAlgo_PaveFiller.hxx
index c9db7dc426..b6ce0d4f1d 100644
--- a/src/BOPAlgo/BOPAlgo_PaveFiller.hxx
+++ b/src/BOPAlgo/BOPAlgo_PaveFiller.hxx
@@ -193,7 +193,7 @@ protected:
      const Standard_Real theTolR3D, const BOPDS_IndexedMapOfPaveBlock& theMPB,
      Handle(BOPDS_PaveBlock)& thePBOut, Standard_Real& theTolNew);
   
-  Standard_EXPORT Standard_Boolean IsExistingPaveBlock (const Handle(BOPDS_PaveBlock)& thePB, const BOPDS_Curve& theNC, const Standard_Real theTolR3D, const BOPCol_ListOfInteger& theLSE);
+  Standard_EXPORT Standard_Boolean IsExistingPaveBlock (const Handle(BOPDS_PaveBlock)& thePB, const BOPDS_Curve& theNC, const BOPCol_ListOfInteger& theLSE);
   
 
   //! Treatment of section edges.
diff --git a/src/BOPAlgo/BOPAlgo_PaveFiller_6.cxx b/src/BOPAlgo/BOPAlgo_PaveFiller_6.cxx
index 49e5ea237d..b978f3bfbc 100644
--- a/src/BOPAlgo/BOPAlgo_PaveFiller_6.cxx
+++ b/src/BOPAlgo/BOPAlgo_PaveFiller_6.cxx
@@ -516,7 +516,7 @@ void BOPAlgo_PaveFiller::MakeBlocks()
           continue;
         }
         //
-        bExist=IsExistingPaveBlock(aPB, aNC, aTolR3D, aLSE);
+        bExist=IsExistingPaveBlock(aPB, aNC, aLSE);
         if (bExist) {
           continue;
         }
@@ -1091,7 +1091,6 @@ Standard_Boolean BOPAlgo_PaveFiller::IsExistingVertex
 Standard_Boolean BOPAlgo_PaveFiller::IsExistingPaveBlock
   (const Handle(BOPDS_PaveBlock)& thePB,
    const BOPDS_Curve& theNC,
-   const Standard_Real theTolR3D,
    const BOPCol_ListOfInteger& theLSE)
 {
   Standard_Boolean bRet=Standard_True;
@@ -1101,16 +1100,24 @@ Standard_Boolean BOPAlgo_PaveFiller::IsExistingPaveBlock
   } 
   //
   Standard_Real aT1, aT2, aTm, aTx, aTol, aDist;
-  Standard_Integer nE, iFlag;
+  Standard_Integer nE, iFlag, nV1, nV2;
   gp_Pnt aPm;
   Bnd_Box aBoxPm;
   BOPCol_ListIteratorOfListOfInteger aItLI;
   //
   thePB->Range(aT1, aT2);
+  thePB->Indices(nV1, nV2);
+  const TopoDS_Vertex &aV1 = TopoDS::Vertex(myDS->Shape(nV1)),
+                      &aV2 = TopoDS::Vertex(myDS->Shape(nV2));
+  const Standard_Real aTolV1 = BRep_Tool::Tolerance(aV1),
+                      aTolV2 = BRep_Tool::Tolerance(aV2);
+
+  aTol = Max(aTolV1, aTolV2);
+
   aTm=IntTools_Tools::IntermediatePoint (aT1, aT2);
   theNC.Curve().D0(aTm, aPm);
   aBoxPm.Add(aPm);
-  aBoxPm.Enlarge(theTolR3D);
+  aBoxPm.Enlarge(aTol);
   //
   aItLI.Initialize(theLSE);
   for (; aItLI.More(); aItLI.Next()) {
@@ -1121,9 +1128,8 @@ Standard_Boolean BOPAlgo_PaveFiller::IsExistingPaveBlock
     const Bnd_Box& aBoxE=aSIE.Box();
     if (!aBoxE.IsOut(aBoxPm)) {
       const TopoDS_Edge& aE=(*(TopoDS_Edge *)(&aSIE.Shape()));
-      aTol = BRep_Tool::Tolerance(aE);
-      aTol = aTol > theTolR3D ? aTol : theTolR3D;
-      iFlag=myContext->ComputePE(aPm, aTol, aE, aTx, aDist);
+      const Standard_Real aTol1 = Max(BRep_Tool::Tolerance(aE), aTol);
+      iFlag=myContext->ComputePE(aPm, aTol1, aE, aTx, aDist);
       if (!iFlag) {
         return bRet;
       }
@@ -1148,32 +1154,38 @@ Standard_Boolean BOPAlgo_PaveFiller::IsExistingPaveBlock
   Standard_Real aT1, aT2, aTm, aTx;
   Standard_Integer nSp, iFlag1, iFlag2, nV11, nV12, nV21, nV22, i, aNbPB;
   gp_Pnt aP1, aPm, aP2;
-  Bnd_Box aBoxP1, aBoxPm, aBoxP2;
+  Bnd_Box aBoxP1, aBoxPm, aBoxP2, aBoxTmp;
   //
   bRet=Standard_False;
   const IntTools_Curve& aIC=theNC.Curve();
   //
   thePB->Range(aT1, aT2);
   thePB->Indices(nV11, nV12);
+  const Standard_Real aTolV11 = BRep_Tool::Tolerance(TopoDS::Vertex(myDS->Shape(nV11)));
+  const Standard_Real aTolV12 = BRep_Tool::Tolerance(TopoDS::Vertex(myDS->Shape(nV12)));
+  const Standard_Real aTolV1 = Max(aTolV11, aTolV12);
+
   //first point
   aIC.D0(aT1, aP1);
   aBoxP1.Add(aP1);
-  aBoxP1.Enlarge(theTolR3D);
+  aBoxP1.Enlarge(aTolV11);
   //intermediate point
   aTm=IntTools_Tools::IntermediatePoint (aT1, aT2);
   aIC.D0(aTm, aPm);
   aBoxPm.Add(aPm);
-  aBoxPm.Enlarge(theTolR3D);
   //last point
   aIC.D0(aT2, aP2);
   aBoxP2.Add(aP2);
-  aBoxP2.Enlarge(theTolR3D);
+  aBoxP2.Enlarge(aTolV12);
   //
   theTolNew = 0.;
   aNbPB = theMPBOnIn.Extent();
   for (i = 1; i <= aNbPB; ++i) {
     const Handle(BOPDS_PaveBlock)& aPB = theMPBOnIn(i);
     aPB->Indices(nV21, nV22);
+    const Standard_Real aTolV21 = BRep_Tool::Tolerance(TopoDS::Vertex(myDS->Shape(nV21)));
+    const Standard_Real aTolV22 = BRep_Tool::Tolerance(TopoDS::Vertex(myDS->Shape(nV22)));
+    const Standard_Real aTolV2 = Max(aTolV21, aTolV22);
     nSp=aPB->Edge();
     if (nSp < 0)
       continue;
@@ -1187,21 +1199,28 @@ Standard_Boolean BOPAlgo_PaveFiller::IsExistingPaveBlock
       (!aBoxSp.IsOut(aBoxP2) ? 1 : 0);
     if (iFlag1 && iFlag2) {
       Standard_Real aDist;
-      if (aBoxSp.IsOut(aBoxPm) || myContext->ComputePE(aPm, 
-                                                       theTolR3D, 
-                                                       aSp, 
-                                                       aTx, theTolNew)) {
+
+      const Standard_Real aRealTol = myDS->IsCommonBlock(aPB) ?
+                                     Max(aTolV1, aTolV2) : theTolR3D;
+
+      aBoxTmp = aBoxPm;
+      aBoxTmp.Enlarge(aRealTol);
+
+      if (aBoxSp.IsOut(aBoxTmp) || myContext->ComputePE(aPm, 
+                                                        aRealTol,
+                                                        aSp, 
+                                                        aTx, theTolNew)) {
         continue;
       }
       //
       if (iFlag1 == 1) {
-        iFlag1 = !myContext->ComputePE(aP1, theTolR3D, aSp, aTx, aDist);
+        iFlag1 = !myContext->ComputePE(aP1, aRealTol, aSp, aTx, aDist);
         if (theTolNew < aDist)
           theTolNew = aDist;
       }
       //
       if (iFlag2 == 1) {
-        iFlag2 = !myContext->ComputePE(aP2, theTolR3D, aSp, aTx, aDist);
+        iFlag2 = !myContext->ComputePE(aP2, aRealTol, aSp, aTx, aDist);
         if (theTolNew < aDist)
           theTolNew = aDist;
       }
@@ -1811,7 +1830,7 @@ void BOPAlgo_PaveFiller::RemoveUsedVertices(BOPDS_Curve& aNC,
     aTolV = BRep_Tool::Tolerance(aVToUpdate);
     aP2 = BRep_Tool::Pnt(aVToUpdate);
     aDist = aP1.Distance(aP2);
-    aTolVNew = aDist - aTolV2;
+    aTolVNew = Max(aDist - aTolV2, aTolR3D);
     //
     if (aTolVNew > aTolV) {
       BRep_Builder aBB;
diff --git a/tests/boolean/bfuse_complex/E4 b/tests/boolean/bfuse_complex/E4
index 0ec76c8849..ebe7fda01d 100644
--- a/tests/boolean/bfuse_complex/E4
+++ b/tests/boolean/bfuse_complex/E4
@@ -1,7 +1,5 @@
 # Original bug : pro14260
 # Date : 21 Sept 98
-puts "TODO #22911 ALL: Faulty shapes in variables faulty_1 to faulty_"
-puts "TODO #22911 ALL: Error : The area of result shape is"
 
 restore [locate_data_file CTO900_pro14260c.rle] c
 restore [locate_data_file pro14260d.rle] d
diff --git a/tests/bugs/modalg_1/bug1255 b/tests/bugs/modalg_1/bug1255
index 7f187f1396..7d9a3e453a 100755
--- a/tests/bugs/modalg_1/bug1255
+++ b/tests/bugs/modalg_1/bug1255
@@ -6,8 +6,6 @@ puts ""
 ## Exception in command 'section'
 ###############################################
 
-puts "TODO #OCC26815 ALL: Error : The length of result shape is"
-
 restore [locate_data_file OCC1255.brep] a 
 checkshape a
 
@@ -16,7 +14,7 @@ mkface f1 p1
 
 bsection result a f1
 
-checkprops result -l 5840.24 
+checkprops result -l 5837.18
 checkshape result
 checksection result
 checkview -display result -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/bugs/modalg_1/bug1255_1 b/tests/bugs/modalg_1/bug1255_1
index d519e05be1..6bd8b69a6e 100755
--- a/tests/bugs/modalg_1/bug1255_1
+++ b/tests/bugs/modalg_1/bug1255_1
@@ -7,8 +7,6 @@ puts ""
 #  (This script tests new topology)
 ###############################################
 
-puts "TODO #OCC26815 ALL: Error : The length of result shape is"
-
 restore [locate_data_file OCC1255.brep] a 
 checkshape a
 
@@ -21,7 +19,7 @@ if { [catch {bop a f1 } ] } {
     bopsection result
 }
 
-checkprops result -l 5840.24 
+checkprops result -l 5837.18
 checkshape result
 checksection result
 checkview -display result -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/bugs/modalg_4/bug697_2 b/tests/bugs/modalg_4/bug697_2
index b00d8b3fe3..f3fbf27ced 100755
--- a/tests/bugs/modalg_4/bug697_2
+++ b/tests/bugs/modalg_4/bug697_2
@@ -1,6 +1,3 @@
-puts "TODO OCC25829 ALL: Error : The area of result shape is"
-puts "TODO OCC25829 ALL: Faulty shapes in variables faulty_1 to"
-
 puts "============"
 puts "OCC697"
 puts "============"
@@ -27,7 +24,7 @@ if { [catch {bfuse result b2 b3} catch_result] } {
    puts "Faulty : an exception was caught"
 }
 
-checkprops result -s 25357.5 
+checkprops result -s 26041.9
 checkshape result
 checkview -display result -2d -path ${imagedir}/${test_image}.png
 
diff --git a/tests/bugs/modalg_4/bug697_4 b/tests/bugs/modalg_4/bug697_4
index 6a5fe0edb8..ee86ee2fb4 100755
--- a/tests/bugs/modalg_4/bug697_4
+++ b/tests/bugs/modalg_4/bug697_4
@@ -1,6 +1,3 @@
-puts "TODO OCC25829 ALL: Error : The area of result shape is"
-puts "TODO OCC25829 ALL: Faulty shapes in variables faulty_1 to"
-
 puts "============"
 puts "OCC697"
 puts "============"
@@ -21,6 +18,6 @@ checkshape b3
 if { [catch {bfuse result b3 b2} catch_result] } {
    puts "Faulty OCC697"
 }
-checkprops result -s 25357.5 
+checkprops result -s 26041.9
 checkshape result
 checkview -display result -3d -path ${imagedir}/${test_image}.png
diff --git a/tests/bugs/modalg_4/bug697_7 b/tests/bugs/modalg_4/bug697_7
index 96fa265724..4462acb572 100755
--- a/tests/bugs/modalg_4/bug697_7
+++ b/tests/bugs/modalg_4/bug697_7
@@ -1,6 +1,3 @@
-puts "TODO OCC25829 ALL: Error : The area of result shape is"
-puts "TODO OCC25829 ALL: Faulty shapes in variables faulty_1 to"
-
 puts "============"
 puts "OCC697"
 puts "============"
@@ -22,6 +19,6 @@ bop b2 b3
 if { [catch {bopfuse result} catch_result] } {
    puts "Faulty OCC697 "
 }
-checkprops result -s 25357.5 
+checkprops result -s 26041.9
 checkshape result
 checkview -display result -3d -path ${imagedir}/${test_image}.png
diff --git a/tests/bugs/modalg_4/bug697_8 b/tests/bugs/modalg_4/bug697_8
index 9557c44ab1..fc23c71d0a 100755
--- a/tests/bugs/modalg_4/bug697_8
+++ b/tests/bugs/modalg_4/bug697_8
@@ -1,6 +1,3 @@
-puts "TODO OCC25829 ALL: Error : The area of result shape is"
-puts "TODO OCC25829 ALL: Faulty shapes in variables faulty_1 to"
-
 puts "============"
 puts "OCC697"
 puts "============"
@@ -22,6 +19,6 @@ bop b3 b2
 if { [catch {bopfuse result} catch_result] } {
    puts "Faulty OCC697"
 }
-checkprops result -s 25357.5 
+checkprops result -s 26041.9
 checkshape result
 checkview -display result -3d -path ${imagedir}/${test_image}.png
diff --git a/tests/bugs/modalg_4/bug772 b/tests/bugs/modalg_4/bug772
index d10aa8cb59..5ac6a9f7c5 100755
--- a/tests/bugs/modalg_4/bug772
+++ b/tests/bugs/modalg_4/bug772
@@ -1,5 +1,3 @@
-puts "TODO OCC26999 ALL: Error : .*The area .*is"
-
 puts "========"
 puts "OCC772"
 puts "SAM1643"
diff --git a/tests/bugs/modalg_6/bug27128 b/tests/bugs/modalg_6/bug27128
new file mode 100644
index 0000000000..ec95d397ea
--- /dev/null
+++ b/tests/bugs/modalg_6/bug27128
@@ -0,0 +1,23 @@
+puts "============"
+puts "OCC27128"
+puts "============"
+puts ""
+###############################
+## The algorithm of sharing edges in Boolean operation should be improved
+###############################
+
+plane pl 0.195808075898442, -0.229262227170656, 4.05546403129991 0 0 1
+psphere s1 pl 0.03101752454
+restore [locate_data_file bug27128-Helix_Pipe.brep] s2
+
+settolerance s1 2.0e-6
+
+bfuse result s1 s2
+checkshape result
+
+smallview
+donly s1
+fit
+donly result
+
+checkview -screenshot -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/bugs/modalg_6/bug27179 b/tests/bugs/modalg_6/bug27179
new file mode 100644
index 0000000000..4148e739a0
--- /dev/null
+++ b/tests/bugs/modalg_6/bug27179
@@ -0,0 +1,31 @@
+puts "============"
+puts "OCC27179"
+puts "============"
+puts ""
+###############################
+## The algorithm of sharing edges in Boolean operation should be improved
+###############################
+
+plane pl 0.195808075898442, -0.229262227170656, 4.05546403129991 0 0 1
+psphere s1 pl 0.03101752454
+restore [locate_data_file bug27128-Helix_Pipe.brep] s2
+
+settolerance s1 2.0e-6
+
+explode s1 f
+explode s2 f
+
+bsection result s1_1 s2_2
+
+smallview
+donly s1
+fit
+donly result
+
+if { [string compare -nocase [checksection result] " nb alone Vertices : 0\n\n"] } {
+  puts "ERROR: the section is not closed"
+} else {
+  puts "The section is OK"
+}
+
+checkview -screenshot -2d -path ${imagedir}/${test_image}.png