diff --git a/Makefile b/Makefile
index 18cb7d15c7..50cef84a21 100755
--- a/Makefile
+++ b/Makefile
@@ -1,5 +1,5 @@
-CC = gcc
-CPP = g++
+CC ?= gcc
+CPP ?= g++
 AR = ar
 LD = ld
 
diff --git a/build-support/factor.sh b/build-support/factor.sh
index d5b8bd5411..e059a7d84f 100755
--- a/build-support/factor.sh
+++ b/build-support/factor.sh
@@ -97,7 +97,7 @@ set_md5sum() {
 set_gcc() {
     case $OS in
         openbsd) ensure_program_installed egcc; CC=egcc;;
-        *) CC=gcc;;
+        *) CC=${CC:=gcc};;
     esac
 }