diff --git a/tests/libtest/lib5000.c b/tests/libtest/lib5000.c
index a0eb92f0ae..05c5b99ac4 100644
--- a/tests/libtest/lib5000.c
+++ b/tests/libtest/lib5000.c
@@ -50,7 +50,9 @@ static CURLcode test_lib5000(const char *URL)
   easy_setopt(curl, CURLOPT_HEADER, 0L);
   easy_setopt(curl, CURLOPT_URL, URL);
   if(libtest_arg2) {
-    connect_to = curl_slist_append(connect_to, libtest_arg2);
+    connect_to = curl_slist_append(NULL, libtest_arg2);
+    if(!connect_to)
+      goto test_cleanup;
   }
   easy_setopt(curl, CURLOPT_CONNECT_TO, connect_to);
 
diff --git a/tests/libtest/lib5004.c b/tests/libtest/lib5004.c
index 33945e867f..767bec410a 100644
--- a/tests/libtest/lib5004.c
+++ b/tests/libtest/lib5004.c
@@ -34,6 +34,7 @@ static CURLcode test_lib5004(const char *URL)
   CURLcode result = TEST_ERR_MAJOR_BAD;
   struct curl_slist *connect_to = NULL;
   struct curl_slist *headers = NULL;
+  struct curl_slist *nheaders;
 
   if(curl_global_init(CURL_GLOBAL_ALL) != CURLE_OK) {
     curl_mfprintf(stderr, "curl_global_init() failed\n");
@@ -60,14 +61,25 @@ static CURLcode test_lib5004(const char *URL)
   headers = curl_slist_append(NULL, "Date: Tue, 20 Apr 2021 02:07:55 GMT");
   if(!headers)
     goto test_cleanup;
-  curl_slist_append(headers, "Content-Type: application/json");
-  curl_slist_append(headers, "Content-Length: 18");
+
+  nheaders = curl_slist_append(headers, "Content-Type: application/json");
+  if(!nheaders)
+    goto test_cleanup;
+  headers = nheaders;
+
+  nheaders = curl_slist_append(headers, "Content-Length: 18");
+  if(!nheaders)
+    goto test_cleanup;
+  headers = nheaders;
+
   easy_setopt(curl, CURLOPT_HTTPHEADER, headers);
 
   easy_setopt(curl, CURLOPT_HEADER, 0L);
   easy_setopt(curl, CURLOPT_URL, URL);
   if(libtest_arg2) {
-    connect_to = curl_slist_append(connect_to, libtest_arg2);
+    connect_to = curl_slist_append(NULL, libtest_arg2);
+    if(!connect_to)
+      goto test_cleanup;
   }
   easy_setopt(curl, CURLOPT_CONNECT_TO, connect_to);