diff --git a/lucene/src/test-framework/org/apache/lucene/search/CheckHits.java b/lucene/src/test-framework/org/apache/lucene/search/CheckHits.java
index dbf6efa910d..3aab5faf06e 100644
--- a/lucene/src/test-framework/org/apache/lucene/search/CheckHits.java
+++ b/lucene/src/test-framework/org/apache/lucene/search/CheckHits.java
@@ -37,6 +37,14 @@ public class CheckHits {
    * this allows for a small amount of relative variation
    */
   public static float EXPLAIN_SCORE_TOLERANCE_DELTA = 0.001f;
+  
+  /**
+   * In general we use a relative epsilon, but some tests do crazy things
+   * like boost documents with 0, creating tiny tiny scores where the
+   * relative difference is large but the absolute difference is tiny.
+   * we ensure the the epsilon is always at least this big.
+   */
+  public static float EXPLAIN_SCORE_TOLERANCE_MINIMUM = 1e-6f;
     
   /**
    * Tests that all documents up to maxDoc which are *not* in the
@@ -306,7 +314,7 @@ public class CheckHits {
   }
 
   private static float explainToleranceDelta(float f1, float f2) {
-    return Math.max(Math.abs(f1), Math.abs(f2)) * EXPLAIN_SCORE_TOLERANCE_DELTA;
+    return Math.max(EXPLAIN_SCORE_TOLERANCE_MINIMUM, Math.max(Math.abs(f1), Math.abs(f2)) * EXPLAIN_SCORE_TOLERANCE_DELTA);
   }
 
   /**