diff --git a/tests/openpgp/Makefile.am b/tests/openpgp/Makefile.am
index f6014c9c5..6423da13c 100644
--- a/tests/openpgp/Makefile.am
+++ b/tests/openpgp/Makefile.am
@@ -78,6 +78,7 @@ XTESTS = \
 	gpgv-forged-keyring.scm \
 	armor.scm \
 	import.scm \
+	import-incomplete.scm \
 	import-revocation-certificate.scm \
 	ecc.scm \
 	4gb-packet.scm \
diff --git a/tests/openpgp/import-incomplete.scm b/tests/openpgp/import-incomplete.scm
new file mode 100755
index 000000000..727a027c6
--- /dev/null
+++ b/tests/openpgp/import-incomplete.scm
@@ -0,0 +1,68 @@
+#!/usr/bin/env gpgscm
+
+;; Copyright (C) 2016 g10 Code GmbH
+;;
+;; This file is part of GnuPG.
+;;
+;; GnuPG is free software; you can redistribute it and/or modify
+;; it under the terms of the GNU General Public License as published by
+;; the Free Software Foundation; either version 3 of the License, or
+;; (at your option) any later version.
+;;
+;; GnuPG is distributed in the hope that it will be useful,
+;; but WITHOUT ANY WARRANTY; without even the implied warranty of
+;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+;; GNU General Public License for more details.
+;;
+;; You should have received a copy of the GNU General Public License
+;; along with this program; if not, see <http://www.gnu.org/licenses/>.
+
+(load (in-srcdir "tests" "openpgp" "defs.scm"))
+(setup-environment)
+
+(call-check `(,(tool 'gpg) --import ,(in-srcdir "tests" "openpgp" "import-incomplete" "primary+uid.asc")))
+
+(info "Test import of new subkey, from a certificate without uid")
+(define keyid "573EA710367356BB")
+(call-check `(,(tool 'gpg) --import ,(in-srcdir "tests" "openpgp" "import-incomplete" "primary+subkey+sub-sig.asc")))
+(tr:do
+ (tr:pipe-do
+  (pipe:gpg `(--list-keys --with-colons ,keyid)))
+ (tr:call-with-content
+  (lambda (c)
+    ;; XXX we do not have a regexp library
+    (unless (any (lambda (line)
+		   (and (string-prefix? line "sub:")
+			(string-contains? line "573EA710367356BB")))
+		 (string-split-newlines c))
+	    (exit 1)))))
+
+(info "Test import of a subkey revocation, from a certificate without uid")
+(define keyid "573EA710367356BB")
+(call-check `(,(tool 'gpg) --import ,(in-srcdir "tests" "openpgp" "import-incomplete" "primary+subkey+sub-revocation.asc")))
+(tr:do
+ (tr:pipe-do
+  (pipe:gpg `(--list-keys --with-colons ,keyid)))
+ (tr:call-with-content
+  (lambda (c)
+    ;; XXX we do not have a regexp library
+    (unless (any (lambda (line)
+		   (and (string-prefix? line "sub:r:")
+			(string-contains? line "573EA710367356BB")))
+		 (string-split-newlines c))
+	    (exit 1)))))
+
+(info "Test import of revocation, from a certificate without uid")
+(call-check `(,(tool 'gpg) --import ,(in-srcdir "tests" "openpgp" "import-incomplete" "primary+revocation.asc")))
+(tr:do
+ (tr:pipe-do
+  (pipe:gpg `(--list-keys --with-colons ,keyid)))
+ (tr:call-with-content
+  (lambda (c)
+    ;; XXX we do not have a regexp library
+    (unless (any (lambda (line)
+		   (and (string-prefix? line "pub:r:")
+			(string-contains? line "0843DA969AA8DAFB")))
+		 (string-split-newlines c))
+	    (exit 1)))))
+
diff --git a/tests/openpgp/import-incomplete/primary+revocation.asc b/tests/openpgp/import-incomplete/primary+revocation.asc
new file mode 100644
index 000000000..6b7b60802
--- /dev/null
+++ b/tests/openpgp/import-incomplete/primary+revocation.asc
@@ -0,0 +1,9 @@
+-----BEGIN PGP PUBLIC KEY BLOCK-----
+Comment: [E] primary key, revocation signature over primary (no user ID)
+
+mDMEXNmUGRYJKwYBBAHaRw8BAQdA75R8VlchvmEd2Iz/8l07RoKUaUPDB71Ao1zZ
+631VAN2IeAQgFggAIBYhBLRpj5W82H/gSMzKKQhD2paaqNr7BQJc2ZQZAh0AAAoJ
+EAhD2paaqNr7qAwA/2jBUpnN0BxwRO/4CrxvrLIsL+C9aSXJUOTv8XkP4lvtAQD3
+XsDFfFNgEueiTfF7HtOGt5LPmRqVvUpQSMVgJJW6CQ==
+=tM90
+-----END PGP PUBLIC KEY BLOCK-----
diff --git a/tests/openpgp/import-incomplete/primary+subkey+sub-revocation.asc b/tests/openpgp/import-incomplete/primary+subkey+sub-revocation.asc
new file mode 100644
index 000000000..83a51a549
--- /dev/null
+++ b/tests/openpgp/import-incomplete/primary+subkey+sub-revocation.asc
@@ -0,0 +1,10 @@
+-----BEGIN PGP PUBLIC KEY BLOCK-----
+Comment: [D] primary key, subkey, subkey revocation (no user ID)
+
+mDMEXNmUGRYJKwYBBAHaRw8BAQdA75R8VlchvmEd2Iz/8l07RoKUaUPDB71Ao1zZ
+631VAN24OARc2ZQhEgorBgEEAZdVAQUBAQdABsd5ha0AWXdXcSmfeiWIfrNcGqQK
+j++lwwWDAOlkVicDAQgHiHgEKBYIACAWIQS0aY+VvNh/4EjMyikIQ9qWmqja+wUC
+XNmnkAIdAgAKCRAIQ9qWmqja+ylaAQDmIKf86BJEq4OpDqU+V9D+wn2cyuxbyWVQ
+3r9LiL9qNwD/QAjyrhSN8L3Mfq+wdTHo5i0yB9ZCCpHLXSbhCqfWZwQ=
+=dwx2
+-----END PGP PUBLIC KEY BLOCK-----
diff --git a/tests/openpgp/import-incomplete/primary+subkey+sub-sig.asc b/tests/openpgp/import-incomplete/primary+subkey+sub-sig.asc
new file mode 100644
index 000000000..dc47a02d8
--- /dev/null
+++ b/tests/openpgp/import-incomplete/primary+subkey+sub-sig.asc
@@ -0,0 +1,10 @@
+-----BEGIN PGP PUBLIC KEY BLOCK-----
+Comment: [B] primary key, subkey, subkey binding sig (no user ID)
+
+mDMEXNmUGRYJKwYBBAHaRw8BAQdA75R8VlchvmEd2Iz/8l07RoKUaUPDB71Ao1zZ
+631VAN24OARc2ZQhEgorBgEEAZdVAQUBAQdABsd5ha0AWXdXcSmfeiWIfrNcGqQK
+j++lwwWDAOlkVicDAQgHiHgEGBYIACAWIQS0aY+VvNh/4EjMyikIQ9qWmqja+wUC
+XNmUIQIbDAAKCRAIQ9qWmqja++vFAP98G1L+1/rWTGbsnxOAV2RocBYIroAvsbkR
+Ly6FdP8YNwEA7jOgT05CoKIe37MstpOz23mM80AK369Ca3JMmKKCQgg=
+=xuDu
+-----END PGP PUBLIC KEY BLOCK-----
diff --git a/tests/openpgp/import-incomplete/primary+uid-sig.asc b/tests/openpgp/import-incomplete/primary+uid-sig.asc
new file mode 100644
index 000000000..134607d0e
--- /dev/null
+++ b/tests/openpgp/import-incomplete/primary+uid-sig.asc
@@ -0,0 +1,10 @@
+-----BEGIN PGP PUBLIC KEY BLOCK-----
+Comment: [C] primary key and self-sig expiring in 2024 (no user ID)
+
+mDMEXNmUGRYJKwYBBAHaRw8BAQdA75R8VlchvmEd2Iz/8l07RoKUaUPDB71Ao1zZ
+631VAN2IlgQTFggAPgIbAwULCQgHAgYVCgkICwIEFgIDAQIeAQIXgBYhBLRpj5W8
+2H/gSMzKKQhD2paaqNr7BQJc2ZR1BQkJZgHcAAoJEAhD2paaqNr79soA/0lWkUsu
+3NLwgbni6EzJxnTzgeNMpljqNpipHAwfix9hAP93AVtFdC8g7hdUZxawobl9lnSN
+9ohXOEBWvdJgVv2YAg==
+=KWIK
+-----END PGP PUBLIC KEY BLOCK-----
diff --git a/tests/openpgp/import-incomplete/primary+uid.asc b/tests/openpgp/import-incomplete/primary+uid.asc
new file mode 100644
index 000000000..055f30086
--- /dev/null
+++ b/tests/openpgp/import-incomplete/primary+uid.asc
@@ -0,0 +1,10 @@
+-----BEGIN PGP PUBLIC KEY BLOCK-----
+Comment: [A] primary key, user ID, and self-sig expiring in 2021
+
+mDMEXNmUGRYJKwYBBAHaRw8BAQdA75R8VlchvmEd2Iz/8l07RoKUaUPDB71Ao1zZ
+631VAN20CHRlc3Qga2V5iJYEExYIAD4WIQS0aY+VvNh/4EjMyikIQ9qWmqja+wUC
+XNmUGQIbAwUJA8JnAAULCQgHAgYVCgkICwIEFgIDAQIeAQIXgAAKCRAIQ9qWmqja
++0G1AQDdQiwhXxjXLMqoth+D4SigVHTJK8ORwifzsy3UE7mPGwD/aZ67XbAF/lgI
+kv2O1Jo0u9BL9RNNF+L0DM7rAFbfMAs=
+=1eII
+-----END PGP PUBLIC KEY BLOCK-----