diff --git a/integration/copy_test.go b/integration/copy_test.go
index 311ac9c6..13f2020f 100644
--- a/integration/copy_test.go
+++ b/integration/copy_test.go
@@ -1305,7 +1305,9 @@ func (s *SkopeoSuite) TestFailureCopySrcWithMirrorsUnavailable(c *check.C) {
 	dir, err := ioutil.TempDir("", "copy-mirror")
 	c.Assert(err, check.IsNil)
 
-	assertSkopeoFails(c, ".*no such host.*",
+	// .invalid domains are, per RFC 6761, supposed to result in NXDOMAIN.
+	// With systemd-resolved (used only via NSS?), we instead seem to get “Temporary failure in name resolution”
+	assertSkopeoFails(c, ".*(no such host|Temporary failure in name resolution).*",
 		"--registries-conf="+regConfFixture, "copy", "docker://invalid.invalid/busybox", "dir:"+dir)
 }
 
@@ -1321,7 +1323,9 @@ func (s *SkopeoSuite) TestFailureCopySrcWithMirrorAndPrefixUnavailable(c *check.
 	dir, err := ioutil.TempDir("", "copy-mirror")
 	c.Assert(err, check.IsNil)
 
-	assertSkopeoFails(c, ".*no such host.*",
+	// .invalid domains are, per RFC 6761, supposed to result in NXDOMAIN.
+	// With systemd-resolved (used only via NSS?), we instead seem to get “Temporary failure in name resolution”
+	assertSkopeoFails(c, ".*(no such host|Temporary failure in name resolution).*",
 		"--registries-conf="+regConfFixture, "copy", "docker://gcr.invalid/wrong/prefix/busybox", "dir:"+dir)
 }