diff --git a/src/ProjLib/ProjLib_CompProjectedCurve.cxx b/src/ProjLib/ProjLib_CompProjectedCurve.cxx
index cca8a61275..d3216c64e5 100644
--- a/src/ProjLib/ProjLib_CompProjectedCurve.cxx
+++ b/src/ProjLib/ProjLib_CompProjectedCurve.cxx
@@ -621,7 +621,7 @@ void ProjLib_CompProjectedCurve::Init()
 
   gp_Pnt Triple, prevTriple;
 
-  //Basic loop  
+  //Basic loop
   while(t <= LastU) 
   {
     // Search for the beginning of a new continuous part
@@ -670,7 +670,8 @@ void ProjLib_CompProjectedCurve::Init()
 #ifdef OCCT_DEBUG_CHRONO
         InitChron(chr_init_point);
 #endif
-        initpoint=InitialPoint(CPoint, t,myCurve,mySurface, myTolU, myTolV, U, V);
+        // PConfusion - use geometric tolerances in extrema / optimization.
+        initpoint=InitialPoint(CPoint, t,myCurve,mySurface, Precision::PConfusion(), Precision::PConfusion(), U, V);
 #ifdef OCCT_DEBUG_CHRONO
         ResultChron(chr_init_point,t_init_point);
         init_point_count++;
@@ -1645,7 +1646,12 @@ void ProjLib_CompProjectedCurve::UpdateTripleByTrapCriteria(gp_Pnt &thePoint) co
     return;
 
   Standard_Real U,V;
-  InitialPoint(myCurve->Value(thePoint.X()), thePoint.X(), myCurve, mySurface, myTolU, myTolV, U, V);
+  Standard_Boolean isDone = 
+    InitialPoint(myCurve->Value(thePoint.X()), thePoint.X(), myCurve, mySurface, 
+                 Precision::PConfusion(), Precision::PConfusion(), U, V);
+
+  if (!isDone)
+    return;
 
   // Restore original position in case of period jump.
   if (mySurface->IsUPeriodic() &&
diff --git a/tests/bugs/moddata_2/bug453_3 b/tests/bugs/moddata_2/bug453_3
index f786f30b74..9445f94b93 100755
--- a/tests/bugs/moddata_2/bug453_3
+++ b/tests/bugs/moddata_2/bug453_3
@@ -1,5 +1,7 @@
 puts "TODO OCC24156 MacOS: Tcl Exception: tolerance ang"
 puts "TODO OCC24156 MacOS: TEST INCOMPLETE"
+puts "TODO OCC27203 ALL: Error: Max tolerance" 
+puts "TODO OCC27203 Linux: Error : The area of result shape is"
 
 puts "========"
 puts "OCC453"
@@ -25,6 +27,8 @@ explode result So
 tcopy result_1 result
 
 dchrono h2 stop
+
+# Check computation time
 set q2 [ dchrono h2 show ]
 regexp {CPU user time: ([-0-9.+eE]+) seconds} $q2 full z2
 puts "$z2"
@@ -34,5 +38,12 @@ if { $z2 > 85 } {
     puts "Elapsed time is less then 85 seconds - OK"      
 }
 
+# Properties check
+checkprops result -s 5.48216e+006
+
+# Tolerance check
+checkmaxtol result -ref 1628.2217761833963
+
+# Visual check
 checkview -display result -2d -path ${imagedir}/${test_image}.png
 
diff --git a/tests/bugs/moddata_3/bug23703 b/tests/bugs/moddata_3/bug23703
index 2328f354f8..43d32248ec 100644
--- a/tests/bugs/moddata_3/bug23703
+++ b/tests/bugs/moddata_3/bug23703
@@ -14,6 +14,10 @@ pcurve f
 
 project c2d c s
 
+# Length check
+checklength c2d -l 6.2831853071795862
+
+# Visual Check
 v2d
 2dfit
 
diff --git a/tests/bugs/moddata_3/bug27133 b/tests/bugs/moddata_3/bug27133
new file mode 100644
index 0000000000..d988795397
--- /dev/null
+++ b/tests/bugs/moddata_3/bug27133
@@ -0,0 +1,23 @@
+puts "================"
+puts "0027133"
+puts "================"
+puts ""
+##############################################################
+# Incorrect result of the normal projection algorithm
+# Oscillation at the edge end
+##############################################################
+
+restore [locate_data_file bug27133_aE.brep] aE
+restore [locate_data_file bug27133_aF.brep] aF
+
+nproject result aE aF
+
+# Result length check.
+checkprops result -l 0.0037337
+
+# Visual check.
+donly result
+smallview
+fit
+display aE aF
+checkview -screenshot -2d -path ${imagedir}/${test_image}.png