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diff --git a/test/integration/test-ubuntu-bug-1304403-obsolete-priority-standard b/test/integration/test-ubuntu-bug-1304403-obsolete-priority-standard
new file mode 100755
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+++ b/test/integration/test-ubuntu-bug-1304403-obsolete-priority-standard
@@ -0,0 +1,50 @@
+#!/bin/sh
+set -e
+
+TESTDIR="$(readlink -f "$(dirname "$0")")"
+. "$TESTDIR/framework"
+
+setupenvironment
+configarchitecture 'i386'
+
+# Regression test for LP: #1304403
+#
+# The issue here is that libkadm5srv-mit8 (priority standard) is replaced
+# by a new libkadm5srv-mit9 and libkbd5-7 breaks on the old -mit8 package.
+# The -mit8 package is no longer downloadable (and hence not upgradeable)
+
+# normal upradable pkg
+#  (libkdb5-7 that breaks on libkadm5srv-mit8 (<< 1.11+dfsg~)
+insertinstalledpackage 'upgradable' 'all' '1.0' '' 'extra'
+insertpackage 'unstable' 'upgradable' 'all' '2.0' 'Breaks: not-downloadable (<< 1.1)' 'optional'
+
+# no longer downloadable pkg (libkadm5srv-mit8, replaced by libkadm5srv-mit9)
+# but priority standard pushes it higher
+insertinstalledpackage 'not-downloadable' 'all' '1.0' '' 'standard'
+
+setupaptarchive
+
+# discourage keeping obsolete high-priority packages …
+testsuccessequal 'Reading package lists...
+Building dependency tree...
+Calculating upgrade...
+The following packages will be REMOVED:
+  not-downloadable
+The following packages will be upgraded:
+  upgradable
+1 upgraded, 0 newly installed, 1 to remove and 0 not upgraded.
+Remv not-downloadable [1.0]
+Inst upgradable [1.0] (2.0 unstable [all])
+Conf upgradable (2.0 unstable [all])' aptget -s dist-upgrade
+
+# … but if it has dependencies we want to keep it as usual
+for i in $(seq 1 10); do
+insertinstalledpackage "depender$i" 'all' '1.0' 'Depends: not-downloadable'
+done
+
+testsuccessequal 'Reading package lists...
+Building dependency tree...
+Calculating upgrade...
+The following packages have been kept back:
+  upgradable
+0 upgraded, 0 newly installed, 0 to remove and 1 not upgraded.' aptget -s dist-upgrade