diff --git a/scripts/docker-apt-clean b/scripts/docker-apt-clean
index 95b970a..af86fd1 100755
--- a/scripts/docker-apt-clean
+++ b/scripts/docker-apt-clean
@@ -9,12 +9,10 @@
 # effect as running `apt-get clean` but circumvents the deadlock.
 
 DIR=/
-STATE=var/lib/apt/
 CACHE=var/cache/apt/
 
 eval $(apt-config shell DIR Dir)
-eval $(apt-config shell STATE Dir::State)
 eval $(apt-config shell CACHE Dir::Cache)
 
-find $DIR$STATE -type f -delete
-find $DIR$CACHE -type f -delete
+find $DIR$CACHE -type f -name '*.deb' -delete
+find $DIR$CACHE -type f -name '*.bin' -delete
diff --git a/scripts/remove-apt-lists b/scripts/remove-apt-lists
new file mode 100644
index 0000000..6e576f8
--- /dev/null
+++ b/scripts/remove-apt-lists
@@ -0,0 +1,17 @@
+#!/bin/sh
+# remove-apt-lists -- to keep Docker image size small
+# Copyright (C) 2017  Olaf Meeuwissen
+#
+# License: GPL-3.0+
+
+# There is no convenient Post-Invoke hook anywhere to hang this onto
+# but it is nice to be able to clean up the package index files when
+# you want to save space.
+
+DIR=/
+STATE=var/lib/apt/
+
+eval $(apt-config shell DIR Dir)
+eval $(apt-config shell STATE Dir::State)
+
+find $DIR$STATE -type f -name '*_dists_*' -delete