diff --git a/clang/CMakeLists.txt b/clang/CMakeLists.txt
index ae8835d..52b8819 100644
--- a/clang/CMakeLists.txt
+++ b/clang/CMakeLists.txt
@@ -621,10 +621,15 @@
     LLVM_ENABLE_PROJECTS
     LLVM_ENABLE_RUNTIMES)
 
-  # We don't need to depend on compiler-rt if we're building instrumented
+  # We don't need to depend on compiler-rt/libcxx if we're building instrumented
   # because the next stage will use the same compiler used to build this stage.
-  if(TARGET compiler-rt AND NOT LLVM_BUILD_INSTRUMENTED)
-    add_dependencies(clang-bootstrap-deps compiler-rt)
+  if(NOT LLVM_BUILD_INSTRUMENTED)
+    if(TARGET compiler-rt)
+      add_dependencies(clang-bootstrap-deps compiler-rt)
+    endif()
+    if(TARGET cxx-headers)
+      add_dependencies(clang-bootstrap-deps cxx-headers)
+    endif()
   endif()
 
   set(C_COMPILER "clang")
diff --git a/clang/runtime/CMakeLists.txt b/clang/runtime/CMakeLists.txt
index af8ab16..9c2f5cd 100644
--- a/clang/runtime/CMakeLists.txt
+++ b/clang/runtime/CMakeLists.txt
@@ -58,8 +58,12 @@
     endif()
   endforeach()
 
+  if(TARGET cxx-headers)
+    set(COMPILER_RT_LIBCXX_DEPENDENCY "cxx-headers")
+  endif()
+
   ExternalProject_Add(compiler-rt
-    DEPENDS llvm-config clang
+    DEPENDS llvm-config clang ${COMPILER_RT_LIBCXX_DEPENDENCY}
     PREFIX ${COMPILER_RT_PREFIX}
     SOURCE_DIR ${COMPILER_RT_SRC_ROOT}
     STAMP_DIR ${STAMP_DIR}