diff --git a/clang-tools-extra/clangd/IncludeCleaner.cpp b/clang-tools-extra/clangd/IncludeCleaner.cpp
--- a/clang-tools-extra/clangd/IncludeCleaner.cpp
+++ b/clang-tools-extra/clangd/IncludeCleaner.cpp
@@ -74,7 +74,8 @@
   // System headers are likely to be standard library headers.
   // Until we have good support for umbrella headers, don't warn about them.
   if (Inc.Written.front() == '<')
-    return tooling::stdlib::Header::named(Inc.Written).has_value();
+    return tooling::stdlib::Header::named(Inc.Written).has_value() &&
+           !(PI && PI->shouldKeep(Inc.HashLine + 1));
   assert(Inc.HeaderID);
   auto HID = static_cast<IncludeStructure::HeaderID>(*Inc.HeaderID);
   auto FE = AST.getSourceManager().getFileManager().getFileRef(
diff --git a/clang-tools-extra/clangd/unittests/IncludeCleanerTests.cpp b/clang-tools-extra/clangd/unittests/IncludeCleanerTests.cpp
--- a/clang-tools-extra/clangd/unittests/IncludeCleanerTests.cpp
+++ b/clang-tools-extra/clangd/unittests/IncludeCleanerTests.cpp
@@ -76,6 +76,8 @@
   auto TU = TestTU::withCode(R"cpp(
     #include <list>
     #include <queue>
+    #include <vector> // IWYU pragma: keep
+    #include <string> // IWYU pragma: export
     std::list<int> x;
   )cpp");
   // Layout of std library impl is not relevant.
@@ -84,10 +86,13 @@
     namespace std {
       template <typename> class list {};
       template <typename> class queue {};
+      template <typename> class vector {};
     }
   )cpp";
   TU.AdditionalFiles["list"] = "#include <bits>";
   TU.AdditionalFiles["queue"] = "#include <bits>";
+  TU.AdditionalFiles["vector"] = "#include <bits>";
+  TU.AdditionalFiles["string"] = "#include <bits>";
   TU.ExtraArgs = {"-isystem", testRoot()};
   auto AST = TU.build();
   IncludeCleanerFindings Findings = computeIncludeCleanerFindings(AST);