diff --git a/lucene/core/src/java/org/apache/lucene/search/RerankKnnFloatVectorQuery.java b/lucene/core/src/java/org/apache/lucene/search/RerankKnnFloatVectorQuery.java
index 753ab22f95d..a7bf7ee5be9 100644
--- a/lucene/core/src/java/org/apache/lucene/search/RerankKnnFloatVectorQuery.java
+++ b/lucene/core/src/java/org/apache/lucene/search/RerankKnnFloatVectorQuery.java
@@ -55,6 +55,10 @@ public class RerankKnnFloatVectorQuery extends Query {
   public Query rewrite(IndexSearcher indexSearcher) throws IOException {
     IndexReader reader = indexSearcher.getIndexReader();
     Query rewritten = indexSearcher.rewrite(query);
+    // short-circuit: don't re-rank if we already got all possible results
+    if (query.getK() <= k) {
+      return rewritten;
+    }
     Weight weight = indexSearcher.createWeight(rewritten, ScoreMode.COMPLETE_NO_SCORES, 1.0f);
     HitQueue queue = new HitQueue(k, false);
     for (var leaf : reader.leaves()) {
diff --git a/lucene/core/src/test/org/apache/lucene/search/TestRerankKnnFloatVectorQuery.java b/lucene/core/src/test/org/apache/lucene/search/TestRerankKnnFloatVectorQuery.java
index fb8c9cf7e91..9f9ee842e6d 100644
--- a/lucene/core/src/test/org/apache/lucene/search/TestRerankKnnFloatVectorQuery.java
+++ b/lucene/core/src/test/org/apache/lucene/search/TestRerankKnnFloatVectorQuery.java
@@ -91,7 +91,7 @@ public class TestRerankKnnFloatVectorQuery extends LuceneTestCase {
       IndexSearcher searcher = new IndexSearcher(reader);
       float[] targetVector = randomFloatVector(VECTOR_DIMENSION, random);
       int k = 10;
-      double oversample = 1.0;
+      double oversample = random.nextFloat(1.5f, 3.0f);
 
       KnnFloatVectorQuery knnQuery =
           new KnnFloatVectorQuery(FIELD, targetVector, k + (int) (k * oversample));