diff --git a/test-suite/tests/sandbox.test b/test-suite/tests/sandbox.test
index 96651a2b1..54fb79495 100644
--- a/test-suite/tests/sandbox.test
+++ b/test-suite/tests/sandbox.test
@@ -40,13 +40,17 @@
 
 (with-test-prefix "time limit"
   (pass-if "0 busy loop"
+    (unless (defined? 'SIGALRM) (throw 'unsupported))
     (call-with-time-limit 0 busy-loop (lambda () #t)))
   (pass-if "0.001 busy loop"
+    (unless (defined? 'SIGALRM) (throw 'unsupported))
     (call-with-time-limit 0.001 busy-loop (lambda () #t)))
   (pass-if "0 sleep"
+    (unless (defined? 'SIGALRM) (throw 'unsupported))
     (call-with-time-limit 0 (lambda () (usleep-loop #e1e6) #f)
                           (lambda () #t)))
   (pass-if "0.001 sleep"
+    (unless (defined? 'SIGALRM) (throw 'unsupported))
     (call-with-time-limit 0.001 (lambda () (usleep-loop #e1e6) #f)
                           (lambda () #t))))
 
diff --git a/test-suite/tests/time.test b/test-suite/tests/time.test
index b5c7dbc36..72ad5bb15 100644
--- a/test-suite/tests/time.test
+++ b/test-suite/tests/time.test
@@ -29,7 +29,9 @@
 
   (for-each (lambda (t)
 	      (pass-if (list "in another thread after error" t)
-		(or (provided? 'threads) (throw 'unsupported))
+		(unless (and (provided? 'threads)
+                             (defined? 'alarm))
+                  (throw 'unsupported))
 
 		(alarm 5)
 		(false-if-exception (gmtime t))