diff --git a/tests/inetd.sh b/tests/inetd.sh
index 0301b68..894ce98 100644
--- a/tests/inetd.sh
+++ b/tests/inetd.sh
@@ -77,6 +77,15 @@ cat > "$conf" <<EOF
                                     (endpoint (make-socket-address
                                                AF_UNIX "$service_socket")))
                                    #:max-connections 5)
+   #:stop  (make-inetd-destructor))
+ (make <service>
+   #:provides '(test-inetd-fail)
+   #:start (make-inetd-constructor '("$(type -P false)")
+                                   (list
+                                    (endpoint (make-socket-address
+                                               AF_INET
+                                               INADDR_LOOPBACK
+                                               $PORT))))
    #:stop  (make-inetd-destructor)))
 
 (start 'test-inetd)
@@ -95,6 +104,11 @@ file_descriptor_count ()
     ls -l /proc/$shepherd_pid/fd/[0-9]* | wc -l
 }
 
+# Trigger startup of the finalizer thread, which creates a couple of pipes.
+# That way, those extra file descriptors won't influence the comparison with
+# INITIAL_FD_COUNT done at the end.
+$herd eval root '(gc)'
+
 initial_fd_count=$(file_descriptor_count)
 
 $herd status test-inetd | grep started
@@ -203,3 +217,16 @@ $herd status
 # At this point, shepherd should have INITIAL_FD_COUNT - 1 file descriptors
 # opened.
 test $(file_descriptor_count) -lt $initial_fd_count
+
+# Now test a service that fails as soon as it's passed an incoming connection.
+$herd start test-inetd-fail
+for i in $(seq 1 10)
+do
+    $herd status
+    test $($herd status | grep '\+' | wc -l) -eq 2
+    ! converse_with_echo_server \
+	"(make-socket-address AF_INET INADDR_LOOPBACK $PORT)"
+done
+
+$herd stop test-inetd-unix
+test $(file_descriptor_count) -lt $initial_fd_count