diff --git a/Number_types/doc_tex/NumberTypeSupport_ref/Sqrt_extension.tex b/Number_types/doc_tex/NumberTypeSupport_ref/Sqrt_extension.tex
index 6a33954c33b..da322c6b147 100644
--- a/Number_types/doc_tex/NumberTypeSupport_ref/Sqrt_extension.tex
+++ b/Number_types/doc_tex/NumberTypeSupport_ref/Sqrt_extension.tex
@@ -143,7 +143,7 @@ $a0 + a1 * sqrt(root)$.
 
 \ccMethod{
 Sqrt_extension compare 
-(const Sqrt_extension& y, bool in_same_extension = false) const;}{
+(const Sqrt_extension& y, bool in_same_extension = true) const;}{
   Compares \ccVar\ with y. \\
   The optional bool \ccc{in_same_extension} indicates whether \ccVar\ 
   and $y$ are in the same extension of NT.
diff --git a/Number_types/include/CGAL/Sqrt_extension/Sqrt_extension_type.h b/Number_types/include/CGAL/Sqrt_extension/Sqrt_extension_type.h
index 72c646b327a..86bb1943709 100644
--- a/Number_types/include/CGAL/Sqrt_extension/Sqrt_extension_type.h
+++ b/Number_types/include/CGAL/Sqrt_extension/Sqrt_extension_type.h
@@ -422,9 +422,11 @@ compare (const NT& num) const {
     return ((Self(a0_ - num, a1_, root_)).sign_());
 }
 
-// compare of two values with different extension
+// compare of two values that may be in different extension
+// However, the default is, that the the numbers are defined over the same
+// extension. 
 CGAL::Comparison_result
-compare(const Self& y, bool in_same_extension = false ) const
+compare(const Self& y, bool in_same_extension = true ) const
 {
     if (! is_extended_)
         return (CGAL::opposite (y.compare (a0_)));
@@ -619,6 +621,13 @@ const Sqrt_extension<NT,ROOT> & y){
   return (std::max)(x,y);
 }
 
+template <class NT, class ROOT> inline 
+CGAL::Comparison_result compare (
+    const Sqrt_extension<NT,ROOT>& x, 
+    const Sqrt_extension<NT,ROOT>& y,
+    bool in_same_extension = true ){
+  return x.compare(y,in_same_extension);
+}
 
 CGAL_END_NAMESPACE
 
diff --git a/Number_types/test/Number_types/Sqrt_extension.cpp b/Number_types/test/Number_types/Sqrt_extension.cpp
index 86f58c8d595..104afa64b6b 100644
--- a/Number_types/test/Number_types/Sqrt_extension.cpp
+++ b/Number_types/test/Number_types/Sqrt_extension.cpp
@@ -339,6 +339,38 @@ void to_double_test(){
         assert(to_interval(ext)==CGAL_NTS to_interval(-3.0) );
     }
 }
+
+//This test is dedicated to the comaprison of numbers from different extensions
+template <class EXT>
+void test_compare(){
+  typedef typename EXT::NT NT;
+  typedef typename EXT::ROOT ROOT;
+
+  EXT a(NT(1),NT(-5),ROOT(7));
+  EXT b(NT(2),NT(8),ROOT(5));
+  EXT c(NT(3),NT(0),ROOT(3));
+  
+  assert(a.compare(b,false)==CGAL::SMALLER);
+  assert(a.compare(c,false)==CGAL::SMALLER);
+  assert(b.compare(c,false)==CGAL::LARGER );
+  assert(a.compare(a,false)==CGAL::EQUAL);
+  assert(b.compare(b,false)==CGAL::EQUAL);
+  assert(c.compare(c,false)==CGAL::EQUAL);
+  assert(a.compare(a,true)==CGAL::EQUAL);
+  assert(b.compare(b,true)==CGAL::EQUAL);
+  assert(c.compare(c,true)==CGAL::EQUAL);
+
+  assert(CGAL::compare(a,b,false)==CGAL::SMALLER);
+  assert(CGAL::compare(a,c,false)==CGAL::SMALLER);
+  assert(CGAL::compare(b,c,false)==CGAL::LARGER );
+  assert(CGAL::compare(a,a,false)==CGAL::EQUAL);
+  assert(CGAL::compare(b,b,false)==CGAL::EQUAL);
+  assert(CGAL::compare(c,c,false)==CGAL::EQUAL);
+  assert(CGAL::compare(a,a,true)==CGAL::EQUAL);
+  assert(CGAL::compare(b,b,true)==CGAL::EQUAL);
+  assert(CGAL::compare(c,c,true)==CGAL::EQUAL);
+}
+
 template <class NT, class ROOT, class Algebraic_type>
 void general_test(){
     typedef typename CGAL::Algebraic_structure_traits<NT>::Is_exact Is_exact; 
@@ -379,6 +411,10 @@ void general_test(){
     io_test<EXT3>();  
    
     to_double_test<EXT1>();
+    
+    test_compare<EXT1>();
+    test_compare<EXT2>();
+    test_compare<EXT3>();
 }