diff --git a/src/net/http/serve_test.go b/src/net/http/serve_test.go
index fd2dd6cea5..6b450d41e3 100644
--- a/src/net/http/serve_test.go
+++ b/src/net/http/serve_test.go
@@ -4943,9 +4943,6 @@ func TestServerSetKeepAlivesEnabledClosesConns(t *testing.T) {
 	}) {
 		t.Fatalf("idle count before SetKeepAlivesEnabled called = %v; want 1", idle0)
 	}
-	if !waitCondition(2*time.Second, 10*time.Millisecond, ts.Config.ExportAllConnsIdle) {
-		t.Fatalf("test server has active conns")
-	}
 
 	ts.Config.SetKeepAlivesEnabled(false)
 
diff --git a/src/net/http/server.go b/src/net/http/server.go
index 8a79a6c6a4..be76c6a9c0 100644
--- a/src/net/http/server.go
+++ b/src/net/http/server.go
@@ -1827,6 +1827,14 @@ func (c *conn) serve(ctx context.Context) {
 		c.setState(c.rwc, StateIdle)
 		c.curReq.Store((*response)(nil))
 
+		if !w.conn.server.doKeepAlives() {
+			// We're in shutdown mode. We might've replied
+			// to the user without "Connection: close" and
+			// they might think they can send another
+			// request, but such is life with HTTP/1.1.
+			return
+		}
+
 		if d := c.server.idleTimeout(); d != 0 {
 			c.rwc.SetReadDeadline(time.Now().Add(d))
 			if _, err := c.bufr.Peek(4); err != nil {