diff --git a/tests/testNonlinearOptimizer.cpp b/tests/testNonlinearOptimizer.cpp
index 57b8090ce..0b42c8336 100644
--- a/tests/testNonlinearOptimizer.cpp
+++ b/tests/testNonlinearOptimizer.cpp
@@ -264,8 +264,8 @@ TEST(NonlinearOptimizer, MoreOptimization) {
 //  params.setVerbosityLM("TRYDELTA");
 //  params.setVerbosity("TERMINATION");
   params.setlambdaUpperBound(1e9);
-  params.setRelativeErrorTol(0);
-  params.setAbsoluteErrorTol(0);
+//  params.setRelativeErrorTol(0);
+//  params.setAbsoluteErrorTol(0);
   //params.setlambdaInitial(10);
 
   {
@@ -281,7 +281,7 @@ TEST(NonlinearOptimizer, MoreOptimization) {
   }
   EXPECT(assert_equal(expected, DoglegOptimizer(fg, init).optimize()));
 
-  cout << "===================================================================================" << endl;
+//  cout << "===================================================================================" << endl;
 
   // Try LM with diagonal damping
   Values initBetter = init;
@@ -300,13 +300,34 @@ TEST(NonlinearOptimizer, MoreOptimization) {
     expectedDiagonal = d + params.lambdaInitial * d;
     EXPECT(assert_equal(expectedDiagonal, damped.hessianDiagonal()));
 
-    // test convergence
+    // test convergence (does not!)
     Values actual = optimizer.optimize();
     EXPECT(assert_equal(expected, actual));
 
-    // Check that the gradient is zero
+    // Check that the gradient is zero (it is not!)
     linear = optimizer.linearize();
     EXPECT(assert_equal(expectedGradient,linear->gradientAtZero()));
+
+    // Check that the gradient is zero for damped system (it is not!)
+    damped = optimizer.buildDampedSystem(*linear);
+    VectorValues actualGradient = damped.gradientAtZero();
+    EXPECT(assert_equal(expectedGradient,actualGradient));
+
+    // Check errors at convergence and errors in direction of gradient (decreases!)
+    EXPECT_DOUBLES_EQUAL(46.0254859,fg.error(actual),1e-5);
+    EXPECT_DOUBLES_EQUAL(44.7490532,fg.error(actual.retract(-0.01*actualGradient)),1e-5);
+
+    // Check that solve yields gradient (it's not equal to gradient, as predicted)
+    VectorValues delta = damped.optimize();
+//    cout << damped.augmentedHessian() << endl;
+    double factor = actualGradient[0][0]/delta[0][0];
+    EXPECT(assert_equal(actualGradient,factor*delta));
+
+    // Still pointing downhill !
+    EXPECT_DOUBLES_EQUAL( 0.0105584,dot(-1*actualGradient,delta),1e-5);
+
+    // Check errors at convergence and errors in direction of solution (does not decreaase!)
+    EXPECT_DOUBLES_EQUAL(46.0254859,fg.error(actual.retract(delta)),1e-5);
   }
 }