diff --git a/lucene/core/src/java/org/apache/lucene/search/BlockMaxConjunctionBulkScorer.java b/lucene/core/src/java/org/apache/lucene/search/BlockMaxConjunctionBulkScorer.java
index 0ea42029787f..e440e386d65e 100644
--- a/lucene/core/src/java/org/apache/lucene/search/BlockMaxConjunctionBulkScorer.java
+++ b/lucene/core/src/java/org/apache/lucene/search/BlockMaxConjunctionBulkScorer.java
@@ -84,7 +84,10 @@ private float computeMaxScore(int windowMin, int windowMax) throws IOException {
   public int score(LeafCollector collector, Bits acceptDocs, int min, int max) throws IOException {
     collector.setScorer(scorable);
 
-    int windowMin = scoreDocFirstUntilDynamicPruning(collector, acceptDocs, min, max);
+    int windowMin = Math.max(lead.docID(), min);
+    if (scorable.minCompetitiveScore == 0) {
+      windowMin = scoreDocFirstUntilDynamicPruning(collector, acceptDocs, min, max);
+    }
 
     while (windowMin < max) {
       // Use impacts of the least costly scorer to compute windows