diff --git a/lib/connect.c b/lib/connect.c
index b9da7c1621..20275163b5 100644
--- a/lib/connect.c
+++ b/lib/connect.c
@@ -547,9 +547,11 @@ static CURLcode baller_start_next(struct Curl_cfilter *cf,
 {
   if(cf->sockindex == FIRSTSOCKET) {
     baller_next_addr(baller);
-    /* If we get inconclusive answers from the server(s), we make
-     * a second iteration over the address list */
-    if(!baller->addr && baller->inconclusive && !baller->rewinded)
+    /* If we get inconclusive answers from the server(s), we start
+     * again until this whole thing times out. This allows us to
+     * connect to servers that are gracefully restarting and the
+     * packet routing to the new instance has not happened yet (e.g. QUIC). */
+    if(!baller->addr && baller->inconclusive)
       baller_rewind(baller);
     baller_start(cf, data, baller, timeoutms);
   }
diff --git a/lib/vquic/curl_ngtcp2.c b/lib/vquic/curl_ngtcp2.c
index b0a100eb66..3b958e2279 100644
--- a/lib/vquic/curl_ngtcp2.c
+++ b/lib/vquic/curl_ngtcp2.c
@@ -129,7 +129,6 @@ struct cf_ngtcp2_ctx {
   nghttp3_settings h3settings;
   struct curltime started_at;        /* time the current attempt started */
   struct curltime handshake_at;      /* time connect handshake finished */
-  struct curltime reconnect_at;      /* time the next attempt should start */
   struct bufc_pool stream_bufcp;     /* chunk pool for streams */
   struct dynbuf scratch;             /* temp buffer for header construction */
   struct Curl_hash streams;          /* hash `data->mid` to `h3_stream_ctx` */
@@ -2311,12 +2310,6 @@ static CURLcode cf_ngtcp2_connect(struct Curl_cfilter *cf,
 
   CF_DATA_SAVE(save, cf, data);
 
-  if(ctx->reconnect_at.tv_sec && Curl_timediff(now, ctx->reconnect_at) < 0) {
-    /* Not time yet to attempt the next connect */
-    CURL_TRC_CF(data, cf, "waiting for reconnect time");
-    goto out;
-  }
-
   if(!ctx->qconn) {
     ctx->started_at = now;
     result = cf_connect_start(cf, data, &pktx);
diff --git a/lib/vquic/curl_osslq.c b/lib/vquic/curl_osslq.c
index ffe3ca0c11..6121b2f893 100644
--- a/lib/vquic/curl_osslq.c
+++ b/lib/vquic/curl_osslq.c
@@ -288,7 +288,6 @@ struct cf_osslq_ctx {
   struct curltime started_at;        /* time the current attempt started */
   struct curltime handshake_at;      /* time connect handshake finished */
   struct curltime first_byte_at;     /* when first byte was recvd */
-  struct curltime reconnect_at;      /* time the next attempt should start */
   struct bufc_pool stream_bufcp;     /* chunk pool for streams */
   struct Curl_hash streams;          /* hash `data->mid` to `h3_stream_ctx` */
   size_t max_stream_window;          /* max flow window for one stream */
@@ -1686,12 +1685,6 @@ static CURLcode cf_osslq_connect(struct Curl_cfilter *cf,
   now = Curl_now();
   CF_DATA_SAVE(save, cf, data);
 
-  if(ctx->reconnect_at.tv_sec && Curl_timediff(now, ctx->reconnect_at) < 0) {
-    /* Not time yet to attempt the next connect */
-    CURL_TRC_CF(data, cf, "waiting for reconnect time");
-    goto out;
-  }
-
   if(!ctx->tls.ossl.ssl) {
     ctx->started_at = now;
     result = cf_osslq_ctx_start(cf, data);
diff --git a/lib/vquic/curl_quiche.c b/lib/vquic/curl_quiche.c
index 9182fe9e47..768a5f2ae1 100644
--- a/lib/vquic/curl_quiche.c
+++ b/lib/vquic/curl_quiche.c
@@ -96,7 +96,6 @@ struct cf_quiche_ctx {
   uint8_t scid[QUICHE_MAX_CONN_ID_LEN];
   struct curltime started_at;        /* time the current attempt started */
   struct curltime handshake_at;      /* time connect handshake finished */
-  struct curltime reconnect_at;      /* time the next attempt should start */
   struct bufc_pool stream_bufcp;     /* chunk pool for streams */
   struct Curl_hash streams;          /* hash `data->mid` to `stream_ctx` */
   curl_off_t data_recvd;
@@ -1406,13 +1405,6 @@ static CURLcode cf_quiche_connect(struct Curl_cfilter *cf,
   *done = FALSE;
   vquic_ctx_update_time(&ctx->q);
 
-  if(ctx->reconnect_at.tv_sec &&
-     Curl_timediff(ctx->q.last_op, ctx->reconnect_at) < 0) {
-    /* Not time yet to attempt the next connect */
-    CURL_TRC_CF(data, cf, "waiting for reconnect time");
-    goto out;
-  }
-
   if(!ctx->qconn) {
     result = cf_quiche_ctx_open(cf, data);
     if(result)
diff --git a/tests/http/test_03_goaway.py b/tests/http/test_03_goaway.py
index cef5840847..26d57bbe32 100644
--- a/tests/http/test_03_goaway.py
+++ b/tests/http/test_03_goaway.py
@@ -36,7 +36,6 @@ from testenv import Env, CurlClient, ExecResult
 log = logging.getLogger(__name__)
 
 
-@pytest.mark.skipif(condition=Env().ci_run, reason="not suitable for CI runs")
 class TestGoAway:
 
     @pytest.fixture(autouse=True, scope='class')
@@ -83,8 +82,6 @@ class TestGoAway:
         proto = 'h3'
         if proto == 'h3' and env.curl_uses_lib('msh3'):
             pytest.skip("msh3 stalls here")
-        if proto == 'h3' and env.curl_uses_lib('quiche'):
-            pytest.skip("does not work in CI, but locally for some reason")
         if proto == 'h3' and env.curl_uses_ossl_quic():
             pytest.skip('OpenSSL QUIC fails here')
         count = 3