diff --git a/3.6/alpine/Dockerfile b/3.6/alpine/Dockerfile
index b16146e7d..5c9c26f84 100644
--- a/3.6/alpine/Dockerfile
+++ b/3.6/alpine/Dockerfile
@@ -58,11 +58,19 @@ RUN set -ex \
 		tk-dev \
 		xz-dev \
 		zlib-dev \
+		libffi-dev \
+		expat-dev \
 # add build deps before removing fetch deps in case there's overlap
 	&& apk del .fetch-deps \
 	\
 	&& cd /usr/src/python \
+	&& rm -r Modules/expat \
+		Modules/zlib \
+		Modules/_ctypes/darwin* \
+		Modules/_ctypes/libffi* \
 	&& ./configure \
+		--with-system-ffi \
+		--with-system-expat \
 		--enable-loadable-sqlite-extensions \
 		--enable-shared \
 	&& make -j$(getconf _NPROCESSORS_ONLN) \
diff --git a/Dockerfile-alpine.template b/Dockerfile-alpine.template
index 79e1cd2e5..65c49c4c8 100644
--- a/Dockerfile-alpine.template
+++ b/Dockerfile-alpine.template
@@ -52,11 +52,19 @@ RUN set -ex \
 		tk-dev \
 		xz-dev \
 		zlib-dev \
+		libffi-dev \
+		expat-dev \
 # add build deps before removing fetch deps in case there's overlap
 	&& apk del .fetch-deps \
 	\
 	&& cd /usr/src/python \
+	&& rm -r Modules/expat \
+		Modules/zlib \
+		Modules/_ctypes/darwin* \
+		Modules/_ctypes/libffi* \
 	&& ./configure \
+		--with-system-ffi \
+		--with-system-expat \
 		--enable-loadable-sqlite-extensions \
 		--enable-shared \
 	&& make -j$(getconf _NPROCESSORS_ONLN) \