diff --git a/lucene/CHANGES.txt b/lucene/CHANGES.txt
index e90ca7c9edb0..3b0f76fb1006 100644
--- a/lucene/CHANGES.txt
+++ b/lucene/CHANGES.txt
@@ -258,6 +258,8 @@ Optimizations
 
 * GITHUB#15083: Use DocValuesSkippers in SortedNumericDocValuesRangeQuery#rewrite(). (Alan Woodward)
 
+* GITHUB#15081: Filter by maxOtherDoc first to reduce the overhead of filterCompetitiveHits. (Ge Song)
+
 Changes in Runtime Behavior
 ---------------------
 * GITHUB#14823: Decrease TieredMergePolicy's default number of segments per
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 21f8af990b85..2a66428dd247 100644
--- a/lucene/core/src/java/org/apache/lucene/search/BlockMaxConjunctionBulkScorer.java
+++ b/lucene/core/src/java/org/apache/lucene/search/BlockMaxConjunctionBulkScorer.java
@@ -172,11 +172,12 @@ private void scoreWindowScoreFirst(
       return;
     }
 
+    int maxOtherDoc = -1;
     for (scorers[0].nextDocsAndScores(max, acceptDocs, docAndScoreBuffer);
         docAndScoreBuffer.size > 0;
         scorers[0].nextDocsAndScores(max, acceptDocs, docAndScoreBuffer)) {
 
-      docAndScoreAccBuffer.copyFrom(docAndScoreBuffer);
+      docAndScoreAccBuffer.copyWithMinDocRequired(docAndScoreBuffer, maxOtherDoc);
 
       for (int i = 1; i < scorers.length; ++i) {
         double sumOfOtherClause = sumOfOtherClauses[i];
@@ -188,6 +189,7 @@ private void scoreWindowScoreFirst(
         }
 
         ScorerUtil.applyRequiredClause(docAndScoreAccBuffer, iterators[i], scorables[i]);
+        maxOtherDoc = Math.max(iterators[i].docID(), maxOtherDoc);
       }
 
       for (int i = 0; i < docAndScoreAccBuffer.size; ++i) {
@@ -196,10 +198,6 @@ private void scoreWindowScoreFirst(
       }
     }
 
-    int maxOtherDoc = -1;
-    for (int i = 1; i < iterators.length; ++i) {
-      maxOtherDoc = Math.max(iterators[i].docID(), maxOtherDoc);
-    }
     if (lead.docID() < maxOtherDoc) {
       lead.advance(maxOtherDoc);
     }
diff --git a/lucene/core/src/java/org/apache/lucene/search/DocAndScoreAccBuffer.java b/lucene/core/src/java/org/apache/lucene/search/DocAndScoreAccBuffer.java
index ed5ffbc3f9a3..36fe7e12c990 100644
--- a/lucene/core/src/java/org/apache/lucene/search/DocAndScoreAccBuffer.java
+++ b/lucene/core/src/java/org/apache/lucene/search/DocAndScoreAccBuffer.java
@@ -74,4 +74,18 @@ public void copyFrom(DocAndFloatFeatureBuffer buffer) {
     }
     this.size = buffer.size;
   }
+
+  public void copyWithMinDocRequired(DocAndFloatFeatureBuffer buffer, int minDocInclusive) {
+    int i = 0;
+    for (; i < buffer.size && buffer.docs[i] < minDocInclusive; ++i) {
+      // skip entries with doc IDs below the minimum
+    }
+    int newSize = buffer.size - i;
+    growNoCopy(newSize);
+    System.arraycopy(buffer.docs, i, docs, 0, newSize);
+    for (int j = i; j < buffer.size; ++j) {
+      scores[j - i] = buffer.features[j];
+    }
+    this.size = newSize;
+  }
 }
diff --git a/lucene/core/src/java/org/apache/lucene/search/MaxScoreBulkScorer.java b/lucene/core/src/java/org/apache/lucene/search/MaxScoreBulkScorer.java
index c723cbe00f13..2de1513b70c6 100644
--- a/lucene/core/src/java/org/apache/lucene/search/MaxScoreBulkScorer.java
+++ b/lucene/core/src/java/org/apache/lucene/search/MaxScoreBulkScorer.java
@@ -246,11 +246,12 @@ private void scoreInnerWindowAsConjunction(LeafCollector collector, Bits acceptD
     assert essentialQueue.size() == 1;
     assert lead1 == essentialQueue.top();
 
+    int maxOtherDoc = -1;
     for (lead1.scorer.nextDocsAndScores(max, acceptDocs, docAndScoreBuffer);
         docAndScoreBuffer.size > 0;
         lead1.scorer.nextDocsAndScores(max, acceptDocs, docAndScoreBuffer)) {
 
-      docAndScoreAccBuffer.copyFrom(docAndScoreBuffer);
+      docAndScoreAccBuffer.copyWithMinDocRequired(docAndScoreBuffer, maxOtherDoc);
 
       for (int i = allScorers.length - 2; i >= firstRequiredScorer; --i) {
 
@@ -264,6 +265,7 @@ private void scoreInnerWindowAsConjunction(LeafCollector collector, Bits acceptD
 
         DisiWrapper scorer = allScorers[i];
         ScorerUtil.applyRequiredClause(docAndScoreAccBuffer, scorer.iterator, scorer.scorable);
+        maxOtherDoc = Math.max(maxOtherDoc, scorer.iterator.docID());
       }
 
       scoreNonEssentialClauses(collector, docAndScoreAccBuffer, firstRequiredScorer);