Index: include/CMakeLists.txt
===================================================================
--- include/CMakeLists.txt
+++ include/CMakeLists.txt
@@ -19,7 +19,7 @@
 if (LIBCXX_INSTALL_HEADERS)
   install(DIRECTORY .
     DESTINATION include/c++/v1
-    COMPONENT libcxx-headers
+    COMPONENT cxx-headers
     FILES_MATCHING
     ${LIBCXX_HEADER_PATTERN}
     PERMISSIONS OWNER_READ OWNER_WRITE GROUP_READ WORLD_READ
@@ -47,17 +47,20 @@
       DESTINATION include/c++/v1
       PERMISSIONS OWNER_READ OWNER_WRITE GROUP_READ WORLD_READ
       RENAME __config
-      COMPONENT libcxx-headers)
+      COMPONENT cxx-headers)
   endif()
 
   if (NOT CMAKE_CONFIGURATION_TYPES)
     # this target is just needed as a placeholder for the distribution target
-    add_custom_target(libcxx-headers)
-    add_custom_target(install-libcxx-headers
-                      DEPENDS libcxx-headers ${generated_config_deps}
+    add_custom_target(cxx-headers)
+    add_custom_target(install-cxx-headers
+                      DEPENDS cxx-headers ${generated_config_deps}
                       COMMAND "${CMAKE_COMMAND}"
-                              -DCMAKE_INSTALL_COMPONENT=libcxx-headers
+                              -DCMAKE_INSTALL_COMPONENT=cxx-headers
                               -P "${CMAKE_BINARY_DIR}/cmake_install.cmake")
+
+    add_custom_target(libcxx-headers)
+    add_custom_target(install-libcxx-headers DEPENDS install-cxx-headers)
   endif()
 
 endif()
Index: lib/CMakeLists.txt
===================================================================
--- lib/CMakeLists.txt
+++ lib/CMakeLists.txt
@@ -225,8 +225,8 @@
     set(experimental_lib cxx_experimental)
   endif()
   install(TARGETS ${LIBCXX_TARGETS} ${experimental_lib}
-    LIBRARY DESTINATION lib${LIBCXX_LIBDIR_SUFFIX} COMPONENT libcxx
-    ARCHIVE DESTINATION lib${LIBCXX_LIBDIR_SUFFIX} COMPONENT libcxx
+    LIBRARY DESTINATION lib${LIBCXX_LIBDIR_SUFFIX} COMPONENT cxx
+    ARCHIVE DESTINATION lib${LIBCXX_LIBDIR_SUFFIX} COMPONENT cxx
     )
   # NOTE: This install command must go after the cxx install command otherwise
   # it will not be executed after the library symlinks are installed.
@@ -248,13 +248,14 @@
       set(experimental_lib_install_target cxx_experimental)
     endif()
     if(LIBCXX_INSTALL_HEADERS)
-      set(header_install_target install-libcxx-headers)
+      set(header_install_target install-cxx-headers)
     endif()
-    add_custom_target(install-libcxx
+    add_custom_target(install-cxx
                       DEPENDS ${lib_install_target}
                               ${experimental_lib_install_target}
                               ${header_install_target}
                       COMMAND "${CMAKE_COMMAND}"
-                      -DCMAKE_INSTALL_COMPONENT=libcxx
+                      -DCMAKE_INSTALL_COMPONENT=cxx
                       -P "${LIBCXX_BINARY_DIR}/cmake_install.cmake")
+    add_custom_target(install-libcxx DEPENDS install-cxx)
 endif()
Index: test/CMakeLists.txt
===================================================================
--- test/CMakeLists.txt
+++ test/CMakeLists.txt
@@ -52,11 +52,13 @@
   set(experimental_dep cxx_experimental)
 endif()
 
-add_lit_testsuite(check-libcxx
+add_lit_testsuite(check-cxx
   "Running libcxx tests"
   ${CMAKE_CURRENT_BINARY_DIR}
   DEPENDS cxx ${experimental_dep})
 
+add_custom_target(check-libcxx DEPENDS check-cxx)
+
 if (LIBCXX_GENERATE_COVERAGE)
   include(CodeCoverage)
   set(output_dir "${CMAKE_CURRENT_BINARY_DIR}/coverage")