diff --git a/libcxx/include/__algorithm/sift_down.h b/libcxx/include/__algorithm/sift_down.h
index 42803e30631fb..088d5e34c374b 100644
--- a/libcxx/include/__algorithm/sift_down.h
+++ b/libcxx/include/__algorithm/sift_down.h
@@ -51,7 +51,7 @@ __sift_down(_RandomAccessIterator __first,
   }
 
   // check if we are in heap-order
-  if (__comp(*__child_i, *__start))
+  if (!__comp(*__start, *__child_i))
     // we are, __start is larger than its largest child
     return;
 
@@ -75,7 +75,7 @@ __sift_down(_RandomAccessIterator __first,
     }
 
     // check if we are in heap-order
-  } while (!__comp(*__child_i, __top));
+  } while (__comp(__top, *__child_i));
   *__start = std::move(__top);
 }
 
diff --git a/libcxx/test/libcxx/algorithms/alg.sorting/alg.heap.operations/make.heap/sift_down_equal_elements.pass.cpp b/libcxx/test/libcxx/algorithms/alg.sorting/alg.heap.operations/make.heap/sift_down_equal_elements.pass.cpp
new file mode 100644
index 0000000000000..83d3c0bd6813f
--- /dev/null
+++ b/libcxx/test/libcxx/algorithms/alg.sorting/alg.heap.operations/make.heap/sift_down_equal_elements.pass.cpp
@@ -0,0 +1,66 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03
+
+// <algorithm>
+
+// template<class Iter>
+//   void make_heap(Iter first, Iter last);
+
+// This test ensures that equivalent elements are not moved or copied when the heap is created.
+
+#include <algorithm>
+#include <cassert>
+#include <vector>
+#include <utility>
+
+struct Stats {
+  int compared = 0;
+  int copied   = 0;
+  int moved    = 0;
+} stats;
+
+struct MyPair {
+  std::pair<int, int> p;
+  MyPair(int a, int b) : p{a, b} {}
+  MyPair(const MyPair& other) : p(other.p) { ++stats.copied; }
+  MyPair(MyPair&& other) : p(other.p) { ++stats.moved; }
+  MyPair& operator=(const MyPair& other) {
+    p = other.p;
+    ++stats.copied;
+    return *this;
+  }
+  MyPair& operator=(MyPair&& other) {
+    p = other.p;
+    ++stats.moved;
+    return *this;
+  }
+  friend bool operator<(const MyPair& lhs, const MyPair& rhs) {
+    ++stats.compared;
+    return lhs.p.first < rhs.p.first;
+  }
+  friend bool operator==(const MyPair& lhs, const MyPair& rhs) { return lhs.p == rhs.p; }
+};
+
+int main(int, char**) {
+  std::vector<MyPair> hp{{42, 1}, {42, 2}, {42, 3}, {42, 4}, {42, 5}, {42, 6}};
+  std::vector<MyPair> original_hp = hp;
+
+  stats = {};
+  std::make_heap(hp.begin(), hp.end());
+
+  assert(stats.copied == 0);
+  assert(stats.moved == 0);
+  assert(stats.compared == static_cast<int>(hp.size()) - 1);
+
+  assert(hp == original_hp);
+  assert(std::is_heap(hp.begin(), hp.end()));
+
+  return 0;
+}