diff --git a/CMakeLists.txt b/CMakeLists.txt
index 3bb15e8c..c9217001 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -437,15 +437,15 @@ if(CMAKE_C_COMPILER_ID MATCHES "AppleClang|Clang|GNU|Intel" AND NOT CMAKE_SYSTEM
     if(APPLE AND CMAKE_C_COMPILER_ID STREQUAL "AppleClang" AND CMAKE_OSX_ARCHITECTURES)   # to support multi-arch binaries (#999)
       set(MI_OPT_ARCH_FLAGS "")
       if("arm64" IN_LIST CMAKE_OSX_ARCHITECTURES)
-        list(APPEND MI_OPT_ARCH_FLAGS "-Xarch_arm64;-march=armv8.1-a;-mtune=native")
+        list(APPEND MI_OPT_ARCH_FLAGS "-Xarch_arm64;-march=armv8.1-a")
       endif()
       if("x86_64" IN_LIST CMAKE_OSX_ARCHITECTURES)
         list(APPEND MI_OPT_ARCH_FLAGS "-Xarch_x86_64;-march=haswell;-Xarch_x86_64;-mavx2")
       endif()
     elseif(MI_ARCH STREQUAL "x64")
-      set(MI_OPT_ARCH_FLAGS "-march=haswell;-mavx2;-mtune=native")    # fast bit scan (since 2013)
+      set(MI_OPT_ARCH_FLAGS "-march=haswell;-mavx2")    # fast bit scan (since 2013)
     elseif(MI_ARCH STREQUAL "arm64")
-      set(MI_OPT_ARCH_FLAGS "-march=armv8.1-a;-mtune=native")         # fast atomics (since 2016)
+      set(MI_OPT_ARCH_FLAGS "-march=armv8.1-a")         # fast atomics (since 2016)
     endif()
   endif()
 endif()