diff --git a/src/main/java/com/manyangled/gibbous/optim/convex/ConvergenceEpsilon.java b/src/main/java/com/manyangled/gibbous/optim/convex/ConvergenceEpsilon.java
index 4c7b5ef..074b964 100644
--- a/src/main/java/com/manyangled/gibbous/optim/convex/ConvergenceEpsilon.java
+++ b/src/main/java/com/manyangled/gibbous/optim/convex/ConvergenceEpsilon.java
@@ -37,5 +37,5 @@ public ConvergenceEpsilon(double eps) {
     }
 
     /** Default convergence epsilon value */
-    public static final double CONVERGENCE_EPSILON_DEFAULT = 1e-10;
+    public static final double CONVERGENCE_EPSILON_DEFAULT = 1e-9;
 }
diff --git a/src/main/java/com/manyangled/gibbous/optim/convex/NewtonOptimizer.java b/src/main/java/com/manyangled/gibbous/optim/convex/NewtonOptimizer.java
index 50ddaf6..8c5db73 100644
--- a/src/main/java/com/manyangled/gibbous/optim/convex/NewtonOptimizer.java
+++ b/src/main/java/com/manyangled/gibbous/optim/convex/NewtonOptimizer.java
@@ -121,8 +121,6 @@ public PointValuePair doOptimize() {
                 KKTSolution sol = kktSolver.solve(hess, grad);
                 if (sol.lambdaSquared <= (2.0 * epsilon)) break;
                 RealVector xDelta = sol.xDelta;
-                // Halt if there is no further movement in solution space
-                if (xDelta.getNorm() < epsilon) break;
                 double gdd = grad.dotProduct(xDelta);
                 RealVector tx = null;
                 double tv = 0.0;
@@ -154,6 +152,8 @@ public PointValuePair doOptimize() {
                 double vprv = v;
                 x = tx;
                 v = tv;
+                // if improvement becomes very small then we are converged
+                if (Math.abs(1.0 - (v / vprv)) < epsilon) break;
                 // Check halting condition if configured
                 if ((halting != null) && halting.checker.converged(
                         getIterations(),
@@ -182,8 +182,6 @@ public PointValuePair doOptimize() {
                 KKTSolution sol = kktSolver.solve(hess, A, AT, grad, A.operate(x).subtract(b));
                 RealVector xDelta = sol.xDelta;
                 RealVector nuDelta = sol.nuPlus.subtract(nu);
-                // Halt if there is no further movement in solution space
-                if (xDelta.getNorm() < epsilon) break;
                 RealVector tx = null;
                 RealVector tnu = null;
                 double tv = 0.0;
@@ -219,6 +217,8 @@ public PointValuePair doOptimize() {
                 x = tx;
                 nu = tnu;
                 v = tv;
+                // if improvement becomes very small then we are converged
+                if (Math.abs(1.0 - (v / vprv)) < epsilon) break;
                 // check halting condition, if it was configured
                 if ((halting != null) && halting.checker.converged(
                         getIterations(),
diff --git a/src/test/java/com/manyangled/gibbous/COTestingUtils.java b/src/test/java/com/manyangled/gibbous/COTestingUtils.java
index 66058f6..346cb6c 100644
--- a/src/test/java/com/manyangled/gibbous/COTestingUtils.java
+++ b/src/test/java/com/manyangled/gibbous/COTestingUtils.java
@@ -26,7 +26,7 @@
 import com.manyangled.gibbous.optim.convex.QuadraticFunction;
 
 public class COTestingUtils {
-    public static final double eps = 1e-9;
+    public static final double eps = 1e-8;
 
     public static QuadraticFunction translatedQF(double h, double[] center) {
         double[] all1 = new double[center.length];