diff --git a/tests/guix-pack-relocatable.sh b/tests/guix-pack-relocatable.sh
index 38dcf1e485..c45a679bb1 100644
--- a/tests/guix-pack-relocatable.sh
+++ b/tests/guix-pack-relocatable.sh
@@ -65,8 +65,15 @@ export relocatable_option
 tarball="`guix pack $relocatable_option -S /Bin=bin sed`"
 (cd "$test_directory"; tar xvf "$tarball")
 
-# Run that relocatable 'sed' in a user namespace where we "erase" the store by
-# mounting an empty file system on top of it.  That way, we exercise the
-# wrapper code that creates the user namespace and bind-mounts the store.
-unshare -mrf sh -c 'mount -t tmpfs none "$STORE_PARENT"; echo "$STORE_PARENT"/*; "$test_directory/Bin/sed" --version > "$test_directory/output"'
+if unshare -r true		# Are user namespaces supported?
+then
+    # Run that relocatable 'sed' in a user namespace where we "erase" the store by
+    # mounting an empty file system on top of it.  That way, we exercise the
+    # wrapper code that creates the user namespace and bind-mounts the store.
+    unshare -mrf sh -c 'mount -t tmpfs none "$STORE_PARENT"; echo "$STORE_PARENT"/*; "$test_directory/Bin/sed" --version > "$test_directory/output"'
+else
+    # Run the relocatable 'sed' in the current namespaces.  This is a weak
+    # test because we're going to access store items from the host store.
+    "$test_directory/Bin/sed" --version > "$test_directory/output"
+fi
 grep 'GNU sed' "$test_directory/output"
diff --git a/tests/guix-pack.sh b/tests/guix-pack.sh
index a43f4d128f..3cd0404748 100644
--- a/tests/guix-pack.sh
+++ b/tests/guix-pack.sh
@@ -1,6 +1,6 @@
 # GNU Guix --- Functional package management for GNU
 # Copyright © 2018 Chris Marusich <cmmarusich@gmail.com>
-# Copyright © 2018 Ludovic Courtès <ludo@gnu.org>
+# Copyright © 2018, 2019 Ludovic Courtès <ludo@gnu.org>
 #
 # This file is part of GNU Guix.
 #
@@ -59,7 +59,7 @@ is_available () {
     type "$1" > /dev/null
 }
 
-if is_available chroot && is_available unshare; then
+if is_available chroot && is_available unshare && unshare -r true; then
     # Verify we can use what we built.
     unshare -r chroot . /opt/gnu/bin/guile --version
     cd -