diff --git a/lucene/core/src/java/org/apache/lucene/util/BitUtil.java b/lucene/core/src/java/org/apache/lucene/util/BitUtil.java
index 850cb2618093..2389e3b0485d 100644
--- a/lucene/core/src/java/org/apache/lucene/util/BitUtil.java
+++ b/lucene/core/src/java/org/apache/lucene/util/BitUtil.java
@@ -303,4 +303,12 @@ public static int zigZagDecode(int i) {
   public static long zigZagDecode(long l) {
     return ((l >>> 1) ^ -(l & 1));
   }
+
+  /**
+   * Return true if, and only if, the provided integer - treated as an unsigned integer - is either
+   * 0 or a power of two.
+   */
+  public static boolean isZeroOrPowerOfTwo(int x) {
+    return (x & (x - 1)) == 0;
+  }
 }
diff --git a/lucene/core/src/java21/org/apache/lucene/store/MemorySegmentIndexInput.java b/lucene/core/src/java21/org/apache/lucene/store/MemorySegmentIndexInput.java
index a0e7e60e99e6..e9f650e6be69 100644
--- a/lucene/core/src/java21/org/apache/lucene/store/MemorySegmentIndexInput.java
+++ b/lucene/core/src/java21/org/apache/lucene/store/MemorySegmentIndexInput.java
@@ -26,6 +26,7 @@
 import java.util.Objects;
 import java.util.Optional;
 import org.apache.lucene.util.ArrayUtil;
+import org.apache.lucene.util.BitUtil;
 import org.apache.lucene.util.GroupVIntUtil;
 
 /**
@@ -57,6 +58,7 @@ abstract class MemorySegmentIndexInput extends IndexInput implements RandomAcces
   MemorySegment
       curSegment; // redundant for speed: segments[curSegmentIndex], also marker if closed!
   long curPosition; // relative to curSegment, not globally
+  int consecutivePrefetchHitCount;
 
   public static MemorySegmentIndexInput newInstance(
       String resourceDescription,
@@ -314,13 +316,22 @@ public void seek(long pos) throws IOException {
 
   @Override
   public void prefetch(long offset, long length) throws IOException {
+    if (NATIVE_ACCESS.isEmpty()) {
+      return;
+    }
+
     ensureOpen();
 
     Objects.checkFromIndexSize(offset, length, length());
 
-    if (NATIVE_ACCESS.isEmpty()) {
+    if (BitUtil.isZeroOrPowerOfTwo(consecutivePrefetchHitCount++) == false) {
+      // We've had enough consecutive hits on the page cache that this number is neither zero nor a
+      // power of two. There is a good chance that a good chunk of this index input is cached in
+      // physical memory. Let's skip the overhead of the madvise system call, we'll be trying again
+      // on the next power of two of the counter.
       return;
     }
+
     final NativeAccess nativeAccess = NATIVE_ACCESS.get();
 
     try {
@@ -344,7 +355,11 @@ public void prefetch(long offset, long length) throws IOException {
       }
 
       final MemorySegment prefetchSlice = segment.asSlice(offset, length);
-      nativeAccess.madviseWillNeed(prefetchSlice);
+      if (prefetchSlice.isLoaded() == false) {
+        // We have a cache miss on at least one page, let's reset the counter.
+        consecutivePrefetchHitCount = 0;
+        nativeAccess.madviseWillNeed(prefetchSlice);
+      }
     } catch (
         @SuppressWarnings("unused")
         IndexOutOfBoundsException e) {
diff --git a/lucene/core/src/test/org/apache/lucene/util/TestBitUtil.java b/lucene/core/src/test/org/apache/lucene/util/TestBitUtil.java
new file mode 100644
index 000000000000..c6c6823fcf8f
--- /dev/null
+++ b/lucene/core/src/test/org/apache/lucene/util/TestBitUtil.java
@@ -0,0 +1,37 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.lucene.util;
+
+import org.apache.lucene.tests.util.LuceneTestCase;
+
+public class TestBitUtil extends LuceneTestCase {
+
+  public void testIsZeroOrPowerOfTwo() {
+    assertTrue(BitUtil.isZeroOrPowerOfTwo(0));
+    for (int shift = 0; shift <= 31; ++shift) {
+      assertTrue(BitUtil.isZeroOrPowerOfTwo(1 << shift));
+    }
+    assertFalse(BitUtil.isZeroOrPowerOfTwo(3));
+    assertFalse(BitUtil.isZeroOrPowerOfTwo(5));
+    assertFalse(BitUtil.isZeroOrPowerOfTwo(6));
+    assertFalse(BitUtil.isZeroOrPowerOfTwo(7));
+    assertFalse(BitUtil.isZeroOrPowerOfTwo(9));
+    assertFalse(BitUtil.isZeroOrPowerOfTwo(Integer.MAX_VALUE));
+    assertFalse(BitUtil.isZeroOrPowerOfTwo(Integer.MAX_VALUE + 2));
+    assertFalse(BitUtil.isZeroOrPowerOfTwo(-1));
+  }
+}