diff --git a/internal/sww/sww_test.go b/internal/sww/sww_test.go
index 84b9b1f..fbff72f 100644
--- a/internal/sww/sww_test.go
+++ b/internal/sww/sww_test.go
@@ -92,6 +92,31 @@ func (o *output) line(t *testing.T, key, value string) map[string]any {
 	return nil
 }
 
+// lineBeforeExit returns the first line whose msg is msg, waiting for it
+// while sww runs. It waits as long as that takes, so that a slow start
+// cannot fail the test, and fails the test if sww exits first.
+func (o *output) lineBeforeExit(
+	t *testing.T, msg string, exited <-chan int,
+) map[string]any {
+	t.Helper()
+
+	for {
+		fields := o.findLine(t, func(fields map[string]any) bool {
+			return fields["msg"] == msg
+		})
+		if fields != nil {
+			return fields
+		}
+
+		select {
+		case status := <-exited:
+			t.Fatalf("exit status %d while waiting for a line with msg %q; output:\n%s",
+				status, msg, o.text())
+		case <-time.After(pollInterval):
+		}
+	}
+}
+
 // findLine returns the first line written so far for which matches is true, or
 // nil.
 func (o *output) findLine(
@@ -236,11 +261,12 @@ func TestServesUntilToldToStop(t *testing.T) {
 	}()
 
 	// The default rule file is read.
-	if rules := out.line(t, "msg", "read the rule files")["rules"]; rules != 12.0 {
+	readRules := out.lineBeforeExit(t, "read the rule files", exited)
+	if rules := readRules["rules"]; rules != 12.0 {
 		t.Errorf("read %v rules from the default rule file, want 12", rules)
 	}
 
-	starting := out.line(t, "msg", "starting")
+	starting := out.lineBeforeExit(t, "starting", exited)
 	wantStartingLine(t, starting, dir)
 
 	addr, _ := starting["address"].(string)
@@ -286,7 +312,7 @@ func TestLogLevelHoldsBackTheLessSevereProcessLines(t *testing.T) {
 		}, out)
 	}()
 
-	out.line(t, "msg", "fetching a list failed")
+	out.lineBeforeExit(t, "fetching a list failed", exited)
 	stop()
 
 	select {
@@ -1261,7 +1287,7 @@ func runUntilStopped(
 		exited <- run(ctx, env, out)
 	}()
 
-	addr, _ := out.line(t, "msg", "starting")["address"].(string)
+	addr, _ := out.lineBeforeExit(t, "starting", exited)["address"].(string)
 	use("http://" + addr + "/")
 	stop()