diff --git a/configure.ac b/configure.ac
index 3b8cda6b8997..a917cfbb0bfd 100644
--- a/configure.ac
+++ b/configure.ac
@@ -5524,17 +5524,18 @@ AC_DEFINE_UNQUOTED(SAL_TYPES_ALIGNMENT8,$SAL_TYPES_ALIGNMENT8)
 dnl ===================================================================
 dnl Check if valgrind headers are available
 dnl ===================================================================
-if test "$cross_compiling" = yes; then
-    ENABLE_VALGRIND=FALSE
-else
+ENABLE_VALGRIND=
+if test "$cross_compiling" != yes; then
     prev_cppflags=$CPPFLAGS
+    # Is VALGRIND_CFLAGS something one is supposed to have in the environment,
+    # or where does it come from?
     CPPFLAGS="$CPPFLAGS $VALGRIND_CFLAGS"
     AC_CHECK_HEADER([valgrind/valgrind.h],
-        [ENABLE_VALGRIND=TRUE],[ENABLE_VALGRIND=FALSE])
+        [ENABLE_VALGRIND=TRUE])
     CPPFLAGS=$prev_cppflags
 fi
 AC_SUBST([ENABLE_VALGRIND])
-if test "$ENABLE_VALGRIND" = FALSE; then
+if test -z "$ENABLE_VALGRIND"; then
     VALGRIND_CFLAGS=
 fi
 AC_SUBST([VALGRIND_CFLAGS])
diff --git a/python3/ExternalProject_python3.mk b/python3/ExternalProject_python3.mk
index 3abf24a0d938..8e7769ba37f6 100644
--- a/python3/ExternalProject_python3.mk
+++ b/python3/ExternalProject_python3.mk
@@ -52,7 +52,7 @@ else
 # specific name like build/lib.linux-x86_64-3.3
 
 python3_cflags = $(ZLIB_CFLAGS)
-ifeq ($(ENABLE_VALGRIND),TRUE)
+ifneq (,$(ENABLE_VALGRIND))
     python3_cflags += $(VALGRIND_CFLAGS)
 endif
 
@@ -60,7 +60,7 @@ $(call gb_ExternalProject_get_state_target,python3,build) :
 	$(call gb_ExternalProject_run,build,\
 		./configure \
 		$(if $(filter YES,$(CROSS_COMPILING)),--build=$(BUILD_PLATFORM) --host=$(HOST_PLATFORM)) \
-		$(if $(filter TRUE,$(ENABLE_VALGRIND)),--with-valgrind) \
+		$(if $(ENABLE_VALGRIND),--with-valgrind) \
 		--prefix=/python-inst \
 		$(if $(filter MACOSX,$(OS)),,--with-system-expat) \
 		$(if $(filter AIX,$(OS)), \