diff --git a/src/ShapeUpgrade/ShapeUpgrade_UnifySameDomain.cxx b/src/ShapeUpgrade/ShapeUpgrade_UnifySameDomain.cxx
index 6d61038dd5..57d9f03d29 100644
--- a/src/ShapeUpgrade/ShapeUpgrade_UnifySameDomain.cxx
+++ b/src/ShapeUpgrade/ShapeUpgrade_UnifySameDomain.cxx
@@ -849,7 +849,9 @@ static Standard_Boolean IsMergingPossible(const TopoDS_Edge& edge1, const TopoDS
 
   if (theLineDirectionOk && t2 == GeomAbs_Line)
   {
-    gp_Vec aCurV(theFirstPoint, BRep_Tool::Pnt(TopExp::LastVertex(edge2, Standard_True)));
+    Standard_Real aLast = (edge2.Orientation() == TopAbs_FORWARD) ?
+      ade2.LastParameter() : ade2.FirstParameter();
+    gp_Vec aCurV(theFirstPoint, ade2.Value(aLast));
     Standard_Real aDD = theDirectionVec.CrossSquareMagnitude(aCurV);
     if (aDD > theLinTol*theLinTol)
       return Standard_False;
@@ -876,8 +878,13 @@ static Standard_Boolean GetLineEdgePoints(const TopoDS_Edge& theInpEdge, gp_Pnt&
   if (aCur->DynamicType() != STANDARD_TYPE(Geom_Line))
     return Standard_False;
 
-  theFirstPoint = BRep_Tool::Pnt(TopExp::FirstVertex(theInpEdge, Standard_True));
-  gp_Pnt aLP = BRep_Tool::Pnt(TopExp::LastVertex(theInpEdge, Standard_True));
+  if (theInpEdge.Orientation() == TopAbs_REVERSED) {
+    Standard_Real tmp = f;
+    f = l;
+    l = tmp;
+  }
+  theFirstPoint = aCur->Value(f);
+  gp_Pnt aLP = aCur->Value(l);
   theDirectionVec = aLP.XYZ().Subtracted(theFirstPoint.XYZ());
   theDirectionVec.Normalize();
   return Standard_True;
diff --git a/tests/bugs/modalg_7/bug27004 b/tests/bugs/modalg_7/bug27004
index 437b0d7e5e..b3b20f524b 100644
--- a/tests/bugs/modalg_7/bug27004
+++ b/tests/bugs/modalg_7/bug27004
@@ -24,7 +24,7 @@ unifysamedom result r
 
 checkshape result
 
-checknbshapes result -vertex 16 -edge 22 -wire 8 -face 8 -solid 1
+checknbshapes result -vertex 12 -edge 18 -wire 8 -face 8 -solid 1
 checkprops result -s 223704 -v 3.27888e+006
 
 checkview -display result -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/bugs/modalg_7/bug29544_1 b/tests/bugs/modalg_7/bug29544_1
new file mode 100644
index 0000000000..11ef52a098
--- /dev/null
+++ b/tests/bugs/modalg_7/bug29544_1
@@ -0,0 +1,15 @@
+puts "========"
+puts "OCC29544"
+puts "========"
+puts ""
+#################################################
+# Regression vs 7.2.0: ShapeUpgrade_UnifySameDomain fails to merge linear edges
+#################################################
+
+restore [locate_data_file bug29544_edges.brep] ce
+unifysamedom result ce
+
+checkshape result
+checkprops result -equal ce
+checknbshapes result -vertex 4 -edge 2
+
diff --git a/tests/bugs/modalg_7/bug29544_2 b/tests/bugs/modalg_7/bug29544_2
new file mode 100644
index 0000000000..52e203b4e2
--- /dev/null
+++ b/tests/bugs/modalg_7/bug29544_2
@@ -0,0 +1,27 @@
+puts "========"
+puts "OCC29544"
+puts "========"
+puts ""
+#################################################
+# Regression vs 7.2.0: ShapeUpgrade_UnifySameDomain fails to merge linear edges
+#################################################
+
+# create edge
+line l 0 0 0 1 0 0
+mkedge e l 0 10
+
+# split edge by the vertex
+vertex v 5 2.e-7 0
+bclearobjects
+bcleartools
+baddobjects e
+baddtools v
+bfillds
+bsplit sp
+
+# unify the splits of the edge
+unifysamedom result sp
+
+checkshape result
+checkprops result -l 10
+checknbshapes result -vertex 2 -edge 1