diff --git a/.CMake/compiler_opts.cmake b/.CMake/compiler_opts.cmake
index 442748439..bf85290d1 100644
--- a/.CMake/compiler_opts.cmake
+++ b/.CMake/compiler_opts.cmake
@@ -22,13 +22,8 @@ if(CMAKE_C_COMPILER_ID MATCHES "Clang|GNU")
     endif()
 
     if(OQS_OPT_TARGET STREQUAL "generic")
-      if(ARCH_X86_64)
-        set(OQS_OPT_FLAG "-march=x86-64")
-      elseif(ARCH_ARM64v8)
-        set(OQS_OPT_FLAG "-mcpu=cortex-a53")
-      elseif(ARCH_ARM32v7)
-        set(OQS_OPT_FLAG "-mcpu=cortex-a5")
-      endif()
+        # Assume sensible default like -march=x86-64, -march=armv8-a, etc.
+        set(OQS_OPT_FLAG "")
     elseif(OQS_OPT_TARGET STREQUAL "auto")
       if(ARCH_X86_64)
           set(OQS_OPT_FLAG "-march=native")