diff --git a/tests/unit/unit1600.c b/tests/unit/unit1600.c
index f0f9cc1f4..af0ad8435 100644
--- a/tests/unit/unit1600.c
+++ b/tests/unit/unit1600.c
@@ -29,7 +29,7 @@ CURL *easy;
 static CURLcode unit_setup(void)
 {
   easy = curl_easy_init();
-  return CURLE_OK;
+  return easy ? CURLE_OK : CURLE_OUT_OF_MEMORY;
 }
 
 static void unit_stop(void)
diff --git a/tests/unit/unit1604.c b/tests/unit/unit1604.c
index 5f1ea9518..a7c2a2543 100644
--- a/tests/unit/unit1604.c
+++ b/tests/unit/unit1604.c
@@ -45,7 +45,7 @@ static void unit_stop(void)
 static char *getflagstr(int flags)
 {
   char *buf = malloc(256);
-  fail_unless(buf, "out of memory");
+  abort_unless(buf, "out of memory");
   snprintf(buf, 256, "%s,%s,%s,%s",
     ((flags & SANITIZE_ALLOW_COLONS) ? "SANITIZE_ALLOW_COLONS" : ""),
     ((flags & SANITIZE_ALLOW_PATH) ? "SANITIZE_ALLOW_PATH" : ""),
@@ -57,7 +57,7 @@ static char *getflagstr(int flags)
 static char *getcurlcodestr(int cc)
 {
   char *buf = malloc(256);
-  fail_unless(buf, "out of memory");
+  abort_unless(buf, "out of memory");
   snprintf(buf, 256, "%s (%d)",
     (cc == SANITIZE_ERR_OK ? "SANITIZE_ERR_OK" :
      cc == SANITIZE_ERR_BAD_ARGUMENT ? "SANITIZE_ERR_BAD_ARGUMENT" :
diff --git a/tests/unit/unit1605.c b/tests/unit/unit1605.c
index c807cb3f2..2fe3a5aca 100644
--- a/tests/unit/unit1605.c
+++ b/tests/unit/unit1605.c
@@ -34,9 +34,10 @@ static void unit_stop(void)
 }
 
 UNITTEST_START
-  CURL *easy = curl_easy_init();
   int len;
   char *esc;
+  CURL *easy = curl_easy_init();
+  abort_unless(easy, "out of memory");
 
   esc = curl_easy_escape(easy, "", -1);
   fail_unless(esc == NULL, "negative string length can't work");
diff --git a/tests/unit/unit1606.c b/tests/unit/unit1606.c
index fdc0ec381..7acba0325 100644
--- a/tests/unit/unit1606.c
+++ b/tests/unit/unit1606.c
@@ -69,6 +69,7 @@ static int runawhile(struct Curl_easy *easy,
 UNITTEST_START
 {
   struct Curl_easy *easy = curl_easy_init();
+  abort_unless(easy, "out of memory");
 
   fail_unless(runawhile(easy, 41, 41, 40, 0) == 41,
               "wrong low speed timeout");