diff --git a/Makefile b/Makefile
index 09e6e39..9addb5d 100644
--- a/Makefile
+++ b/Makefile
@@ -46,9 +46,8 @@ CLANG_WARNINGS := \
 	-Wno-self-assign-overloaded
 WARNINGS := $(BASE_WARNINGS) $($(COMPILER)_WARNINGS)
 
-BASE_CXXFLAGS = -std=gnu++17 -g -O$(OPTLEVEL) \
+BASE_CXXFLAGS = -std=gnu++17 -g \
 	-fwrapv -fno-strict-aliasing -pipe \
-	-march=x86-64 -mtune=generic \
 	-fvisibility=hidden \
 	$(WARNINGS) \
 	-DPY_MAJOR_VERSION=$(PY_MAJOR_VERSION) \
@@ -58,7 +57,7 @@ BASE_CXXFLAGS = -std=gnu++17 -g -O$(OPTLEVEL) \
 	-DLIBPY_MICRO_VERSION=$(MICRO_VERSION)
 GCC_FLAGS = -fmax-errors=$(MAX_ERRORS)
 CLANG_FLAGS = -ferror-limit=$(MAX_ERRORS)
-CXXFLAGS = $(BASE_CXXFLAGS) $($(COMPILER)_FLAGS)
+CXXFLAGS += $(BASE_CXXFLAGS) $($(COMPILER)_FLAGS)
 
 # https://github.com/quantopian/libpy/pull/86/files#r309288697
 INCLUDE_DIRS := include/ \