diff --git a/lucene/CHANGES.txt b/lucene/CHANGES.txt
index 13a5e1f4b3a..b54fa3ff262 100644
--- a/lucene/CHANGES.txt
+++ b/lucene/CHANGES.txt
@@ -82,6 +82,9 @@ Improvements
 * LUCENE-8631: The Korean's user dictionary now picks the longest-matching word and discards
   the other matches. (Yeongsu Kim via Jim Ferenczi)
 
+* LUCENE-8732: ConstantScoreQuery can now early terminate the query if the minimum score is
+  greater than the constant score and total hits are not requested. (Jim Ferenczi)
+
 Changes in Runtime Behavior
 
 * LUCENE-8671: Load FST off-heap also for ID-like fields if reader is not opened
diff --git a/lucene/core/src/java/org/apache/lucene/search/ConstantScoreQuery.java b/lucene/core/src/java/org/apache/lucene/search/ConstantScoreQuery.java
index 9ad256d59fa..74e1f3abd4a 100644
--- a/lucene/core/src/java/org/apache/lucene/search/ConstantScoreQuery.java
+++ b/lucene/core/src/java/org/apache/lucene/search/ConstantScoreQuery.java
@@ -18,8 +18,6 @@ package org.apache.lucene.search;
 
 
 import java.io.IOException;
-import java.util.Collection;
-import java.util.Collections;
 import java.util.Objects;
 
 import org.apache.lucene.index.IndexReader;
@@ -115,9 +113,11 @@ public final class ConstantScoreQuery extends Query {
     final Weight innerWeight = searcher.createWeight(query, ScoreMode.COMPLETE_NO_SCORES, 1f);
     if (scoreMode.needsScores()) {
       return new ConstantScoreWeight(this, boost) {
-
         @Override
         public BulkScorer bulkScorer(LeafReaderContext context) throws IOException {
+          if (scoreMode == ScoreMode.TOP_SCORES) {
+            return super.bulkScorer(context);
+          }
           final BulkScorer innerScorer = innerWeight.bulkScorer(context);
           if (innerScorer == null) {
             return null;
@@ -135,21 +135,12 @@ public final class ConstantScoreQuery extends Query {
             @Override
             public Scorer get(long leadCost) throws IOException {
               final Scorer innerScorer = innerScorerSupplier.get(leadCost);
-              final float score = score();
-              return new FilterScorer(innerScorer) {
-                @Override
-                public float score() throws IOException {
-                  return score;
-                }
-                @Override
-                public float getMaxScore(int upTo) throws IOException {
-                  return score;
-                }
-                @Override
-                public Collection<ChildScorable> getChildren() {
-                  return Collections.singleton(new ChildScorable(innerScorer, "constant"));
-                }
-              };
+              final TwoPhaseIterator twoPhaseIterator = innerScorer.twoPhaseIterator();
+              if (twoPhaseIterator == null) {
+                return new ConstantScoreScorer(innerWeight, score(), scoreMode, innerScorer.iterator());
+              } else {
+                return new ConstantScoreScorer(innerWeight, score(), scoreMode, twoPhaseIterator);
+              }
             }
 
             @Override
diff --git a/lucene/core/src/test/org/apache/lucene/search/TestConstantScoreScorer.java b/lucene/core/src/test/org/apache/lucene/search/TestConstantScoreScorer.java
index 723023137e1..82d6632330f 100644
--- a/lucene/core/src/test/org/apache/lucene/search/TestConstantScoreScorer.java
+++ b/lucene/core/src/test/org/apache/lucene/search/TestConstantScoreScorer.java
@@ -19,9 +19,13 @@ package org.apache.lucene.search;
 import java.io.IOException;
 import java.util.List;
 
+import org.apache.lucene.analysis.Analyzer;
+import org.apache.lucene.analysis.MockAnalyzer;
 import org.apache.lucene.document.Document;
 import org.apache.lucene.document.Field;
+import org.apache.lucene.index.DirectoryReader;
 import org.apache.lucene.index.IndexReader;
+import org.apache.lucene.index.IndexWriter;
 import org.apache.lucene.index.LeafReaderContext;
 import org.apache.lucene.index.RandomIndexWriter;
 import org.apache.lucene.index.Term;
@@ -216,4 +220,38 @@ public class TestConstantScoreScorer extends LuceneTestCase {
       directory.close();
     }
   }
+
+  public void testEarlyTermination() throws IOException {
+    Analyzer analyzer = new MockAnalyzer(random());
+    Directory dir = newDirectory();
+    IndexWriter iw = new IndexWriter(dir, newIndexWriterConfig(analyzer).setMaxBufferedDocs(2).setMergePolicy(newLogMergePolicy()));
+    final int numDocs = 50;
+    for (int i = 0; i < numDocs; i++) {
+      Document doc = new Document();
+      Field f = newTextField("key", i % 2 == 0 ? "foo bar" : "baz", Field.Store.YES);
+      doc.add(f);
+      iw.addDocument(doc);
+    }
+    IndexReader ir = DirectoryReader.open(iw);
+
+    IndexSearcher is = newSearcher(ir);
+
+    TopScoreDocCollector c = TopScoreDocCollector.create(10, null, 10);
+    is.search(new ConstantScoreQuery(new TermQuery(new Term("key", "foo"))), c);
+    assertEquals(11, c.totalHits);
+    assertEquals(TotalHits.Relation.GREATER_THAN_OR_EQUAL_TO, c.totalHitsRelation);
+
+    c = TopScoreDocCollector.create(10, null, 10);
+    Query query = new BooleanQuery.Builder()
+        .add(new ConstantScoreQuery(new TermQuery(new Term("key", "foo"))), Occur.SHOULD)
+        .add(new ConstantScoreQuery(new TermQuery(new Term("key", "bar"))), Occur.FILTER)
+        .build();
+    is.search(query, c);
+    assertEquals(11, c.totalHits);
+    assertEquals(TotalHits.Relation.GREATER_THAN_OR_EQUAL_TO, c.totalHitsRelation);
+
+    iw.close();
+    ir.close();
+    dir.close();
+  }
 }
diff --git a/lucene/facet/src/test/org/apache/lucene/facet/range/TestRangeFacetCounts.java b/lucene/facet/src/test/org/apache/lucene/facet/range/TestRangeFacetCounts.java
index 441675c9e47..7a4367a7fe7 100644
--- a/lucene/facet/src/test/org/apache/lucene/facet/range/TestRangeFacetCounts.java
+++ b/lucene/facet/src/test/org/apache/lucene/facet/range/TestRangeFacetCounts.java
@@ -496,7 +496,7 @@ public class TestRangeFacetCounts extends FacetTestCase {
         } else {
           ddq.add("field", range.getQuery(fastMatchQuery, vs));
         }
-        assertEquals(expectedCounts[rangeID], s.search(ddq, 10).totalHits.value);
+        assertEquals(expectedCounts[rangeID], s.count(ddq));
       }
     }
 
@@ -640,7 +640,7 @@ public class TestRangeFacetCounts extends FacetTestCase {
           ddq.add("field", range.getQuery(fastMatchFilter, vs));
         }
 
-        assertEquals(expectedCounts[rangeID], s.search(ddq, 10).totalHits.value);
+        assertEquals(expectedCounts[rangeID], s.count(ddq));
       }
     }