diff --git a/debian/changelog b/debian/changelog
index ec0d6209..71a5f044 100644
--- a/debian/changelog
+++ b/debian/changelog
@@ -1,5 +1,14 @@
 livecd-rootfs (2.454) UNRELEASED; urgency=medium
 
+  [ Robert C Jennings ]
+  * live-build/ubuntu-cpc/functions: Add a function, teardown_mountpoint,
+    to reverse the work done in setup_mountpoint.  Lack of this function
+    has forced users of setup_mountpoint to implement this separately
+    and the implementations have diverged. (LP: #1716992)
+  * live-build/ubuntu-cpc/functions: Remove umount_settle function.
+    The was only used where teardown_mountpoint was lacking.
+
+  [ Steve Langasek ]
   * live-build/functions: mount tmpfs on /var/cache/apt and var/lib/apt, so
     we don't have to leave empty space in our derivative images for packages
     that have been downloaded/installed/removed.  This normally isn't
diff --git a/live-build/functions b/live-build/functions
index 868fcdb2..fbd8b44c 100644
--- a/live-build/functions
+++ b/live-build/functions
@@ -91,6 +91,21 @@ setup_mountpoint() {
 
 }
 
+teardown_mountpoint() {
+    # Reverse the operations from setup_mountpoint
+    local mountpoint="$1"
+
+    umount "$mountpoint/var/cache/apt"
+    umount "$mountpoint/var/lib/apt"
+    umount "$mountpoint/tmp"
+    umount "$mountpoint/sys"
+    umount "$mountpoint/proc"
+    umount -R "$mountpoint/dev"
+    udevadm settle
+    sleep 3
+    mv resolv.conf.tmp "$mountpoint/etc/resolv.conf"
+}
+
 mount_partition() {
     partition="$1"
     mountpoint="$2"
@@ -134,16 +149,9 @@ EOF
 
 }
 
-umount_settle() {
-    # Unmount device, and let it settle
-    umount $1
-    udevadm settle
-}
-
 umount_partition() {
     local mountpoint=${1}
-    mv resolv.conf.tmp "$mountpoint/etc/resolv.conf"
-    umount -R $mountpoint
+    teardown_mountpoint $mountpoint
     udevadm settle
 
     if [ -n "${rootfs_dev_mapper}" -a -b "${rootfs_dev_mapper}" ]; then
diff --git a/live-build/ubuntu-cpc/hooks/032-root-squashfs.binary b/live-build/ubuntu-cpc/hooks/032-root-squashfs.binary
index 703b2b15..bcce0a76 100755
--- a/live-build/ubuntu-cpc/hooks/032-root-squashfs.binary
+++ b/live-build/ubuntu-cpc/hooks/032-root-squashfs.binary
@@ -36,13 +36,7 @@ chroot binary/boot/squashfs.dir mkdir /lib/modules
 chroot binary/boot/squashfs.dir rm /usr/sbin/grub-probe
 chroot binary/boot/squashfs.dir dpkg-divert --remove --local --rename /usr/sbin/grub-probe
 
-mv resolv.conf.tmp "binary/boot/squashfs.dir/etc/resolv.conf"
-umount "binary/boot/squashfs.dir/proc"
-umount "binary/boot/squashfs.dir/sys"
-umount -R "binary/boot/squashfs.dir/dev"
-umount "binary/boot/squashfs.dir/tmp"
-umount "binary/boot/squashfs.dir/var/lib/apt"
-umount "binary/boot/squashfs.dir/var/cache/apt"
+teardown_mountpoint binary/boot/squashfs.dir
 
 squashfs_f="${PWD}/livecd.ubuntu-cpc.squashfs"
 squashfs_f_manifest="${squashfs_f}.manifest"