diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h
index 6ff689de39..3ab8a4c8ab 100644
--- a/Eigen/src/SVD/JacobiSVD.h
+++ b/Eigen/src/SVD/JacobiSVD.h
@@ -425,18 +425,19 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
   JacobiRotation<RealScalar> rot1;
   RealScalar t = m.coeff(0,0) + m.coeff(1,1);
   RealScalar d = m.coeff(1,0) - m.coeff(0,1);
-  if(t == RealScalar(0))
+  
+  if(d == RealScalar(0))
   {
-    rot1.c() = RealScalar(0);
-    rot1.s() = d > RealScalar(0) ? RealScalar(1) : RealScalar(-1);
+    rot1.s() = RealScalar(0);
+    rot1.c() = RealScalar(1);
   }
   else
   {
-    RealScalar t2d2 = numext::hypot(t,d);
-    rot1.c() = abs(t)/t2d2;
-    rot1.s() = d/t2d2;
-    if(t<RealScalar(0))
-      rot1.s() = -rot1.s();
+    // If d!=0, then t/d cannot overflow because the magnitude of the
+    // entries forming d are not too small compared to the ones forming t.
+    RealScalar u = t / d;
+    rot1.s() = RealScalar(1) / sqrt(RealScalar(1) + numext::abs2(u));
+    rot1.c() = rot1.s() * u;
   }
   m.applyOnTheLeft(0,1,rot1);
   j_right->makeJacobi(m,0,1);
diff --git a/test/jacobisvd.cpp b/test/jacobisvd.cpp
index 7dbb29c594..cd04db5be9 100644
--- a/test/jacobisvd.cpp
+++ b/test/jacobisvd.cpp
@@ -354,11 +354,33 @@ void jacobisvd_underoverflow()
   Matrix2d M;
   M << -7.90884e-313, -4.94e-324,
                  0, 5.60844e-313;
+  JacobiSVD<Matrix2d> svd;
+  svd.compute(M,ComputeFullU|ComputeFullV);
+  jacobisvd_check_full(M,svd);
+  
+  VectorXd value_set(9);
+  value_set << 0, 1, -1, 5.60844e-313, -5.60844e-313, 4.94e-324, -4.94e-324, -4.94e-223, 4.94e-223;
+  Array4i id(0,0,0,0);
+  int k = 0;
+  do
+  {
+    M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
+    svd.compute(M,ComputeFullU|ComputeFullV);
+    jacobisvd_check_full(M,svd);
+    
+    id(k)++;
+    if(id(k)>=value_set.size())
+    {
+      while(k<3 && id(k)>=value_set.size()) id(++k)++;
+      id.head(k).setZero();
+      k=0;
+    }
+    
+  } while((id<int(value_set.size())).all());
+  
 #if defined __INTEL_COMPILER
 #pragma warning pop
 #endif
-  JacobiSVD<Matrix2d> svd;
-  svd.compute(M); // just check we don't loop indefinitely
   
   // Check for overflow:
   Matrix3d M3;
@@ -367,7 +389,8 @@ void jacobisvd_underoverflow()
        -8.7190887618028355e+307, -7.3453213709232193e+307, -2.4367363684472105e+307;
 
   JacobiSVD<Matrix3d> svd3;
-  svd3.compute(M3); // just check we don't loop indefinitely
+  svd3.compute(M3,ComputeFullU|ComputeFullV); // just check we don't loop indefinitely
+  jacobisvd_check_full(M3,svd3);
 }
 
 void jacobisvd_preallocate()