diff --git a/public/java/src/org/broadinstitute/sting/gatk/walkers/variantrecalibration/GaussianMixtureModel.java b/public/java/src/org/broadinstitute/sting/gatk/walkers/variantrecalibration/GaussianMixtureModel.java
index 3fa9c3883..82776ca2e 100755
--- a/public/java/src/org/broadinstitute/sting/gatk/walkers/variantrecalibration/GaussianMixtureModel.java
+++ b/public/java/src/org/broadinstitute/sting/gatk/walkers/variantrecalibration/GaussianMixtureModel.java
@@ -52,6 +52,7 @@ public class GaussianMixtureModel {
     private final double[] empiricalMu;
     private final Matrix empiricalSigma;
     public boolean isModelReadyForEvaluation;
+    public boolean failedToConverge = false;
 
     public GaussianMixtureModel( final int numGaussians, final int numAnnotations,
                                  final double shrinkage, final double dirichletParameter, final double priorCounts ) {
diff --git a/public/java/src/org/broadinstitute/sting/gatk/walkers/variantrecalibration/VariantRecalibrator.java b/public/java/src/org/broadinstitute/sting/gatk/walkers/variantrecalibration/VariantRecalibrator.java
index f60a94a22..20b000978 100755
--- a/public/java/src/org/broadinstitute/sting/gatk/walkers/variantrecalibration/VariantRecalibrator.java
+++ b/public/java/src/org/broadinstitute/sting/gatk/walkers/variantrecalibration/VariantRecalibrator.java
@@ -309,8 +309,23 @@ public class VariantRecalibrator extends RodWalker<ExpandingArrayList<VariantDat
         engine.evaluateData( dataManager.getData(), goodModel, false );
 
         // Generate the negative model using the worst performing data and evaluate each variant contrastively
-        final GaussianMixtureModel badModel = engine.generateModel( dataManager.selectWorstVariants( VRAC.PERCENT_BAD_VARIANTS, VRAC.MIN_NUM_BAD_VARIANTS ) );
+        final ExpandingArrayList<VariantDatum> negativeTrainingData = dataManager.selectWorstVariants( VRAC.PERCENT_BAD_VARIANTS, VRAC.MIN_NUM_BAD_VARIANTS );
+        GaussianMixtureModel badModel = engine.generateModel( negativeTrainingData );
         engine.evaluateData( dataManager.getData(), badModel, true );
+
+        // Detect if the negative model failed to converge because of too few points and/or too many Gaussians and try again
+        while( badModel.failedToConverge && VRAC.MAX_GAUSSIANS > 4 ) {
+            logger.info("Negative model failed to converge. Retrying...");
+            VRAC.MAX_GAUSSIANS--;
+            badModel = engine.generateModel( negativeTrainingData );
+            engine.evaluateData( dataManager.getData(), goodModel, false );
+            engine.evaluateData( dataManager.getData(), badModel, true );
+        }
+
+        if( badModel.failedToConverge || goodModel.failedToConverge ) {
+            throw new UserException("NaN LOD value assigned. Clustering with this few variants and these annotations is unsafe. Please consider raising the number of variants used to train the negative model (via --percentBadVariants 0.05, for example) or lowering the maximum number of Gaussians to use in the model (via --maxGaussians 4, for example)");
+        }
+
         engine.calculateWorstPerformingAnnotation( dataManager.getData(), goodModel, badModel );
 
         // Find the VQSLOD cutoff values which correspond to the various tranches of calls requested by the user
diff --git a/public/java/src/org/broadinstitute/sting/gatk/walkers/variantrecalibration/VariantRecalibratorEngine.java b/public/java/src/org/broadinstitute/sting/gatk/walkers/variantrecalibration/VariantRecalibratorEngine.java
index adfb38a25..6d2ac643b 100755
--- a/public/java/src/org/broadinstitute/sting/gatk/walkers/variantrecalibration/VariantRecalibratorEngine.java
+++ b/public/java/src/org/broadinstitute/sting/gatk/walkers/variantrecalibration/VariantRecalibratorEngine.java
@@ -67,14 +67,20 @@ public class VariantRecalibratorEngine {
 
     public void evaluateData( final List<VariantDatum> data, final GaussianMixtureModel model, final boolean evaluateContrastively ) {
         if( !model.isModelReadyForEvaluation ) {
-            model.precomputeDenominatorForEvaluation();
+            try {
+                model.precomputeDenominatorForEvaluation();
+            } catch( Exception e ) {
+                model.failedToConverge = true;
+                return;
+            }
         }
         
         logger.info("Evaluating full set of " + data.size() + " variants...");
         for( final VariantDatum datum : data ) {
             final double thisLod = evaluateDatum( datum, model );
             if( Double.isNaN(thisLod) ) {
-                throw new UserException("NaN LOD value assigned. Clustering with this few variants and these annotations is unsafe. Please consider raising the number of variants used to train the negative model (via --percentBadVariants 0.05, for example) or lowering the maximum number of Gaussians to use in the model (via --maxGaussians 4, for example)");
+                model.failedToConverge = true;
+                return;
             }
 
             datum.lod = ( evaluateContrastively ?