diff --git a/t/005-exit.t b/t/005-exit.t
index 0783c69295..0eff119bc7 100644
--- a/t/005-exit.t
+++ b/t/005-exit.t
@@ -124,6 +124,7 @@ GET /api?user=agentz
 
 === TEST 6: working with ngx_auth_request (simplest form, w/o ngx_memc)
 --- skip_eval: 3:$ENV{TEST_NGINX_USE_HTTP3}
+--- no_http2
 --- http_config eval
 "
     lua_package_cpath '$::LuaCpath';
@@ -197,6 +198,7 @@ Logged in 56
 
 === TEST 7: working with ngx_auth_request (simplest form)
 --- skip_eval: 3:$ENV{TEST_NGINX_USE_HTTP3}
+--- no_http2
 --- http_config eval
 "
     lua_package_cpath '$::LuaCpath';
diff --git a/t/014-bugs.t b/t/014-bugs.t
index d34f42e23d..303187929f 100644
--- a/t/014-bugs.t
+++ b/t/014-bugs.t
@@ -201,7 +201,7 @@ https://datatracker.ietf.org/doc/html/rfc7540#section-8.1.2
    header field names MUST be converted to lowercase prior to their
    encoding in HTTP/2.  A request or response containing uppercase
    header field names MUST be treated as malformed
-
+--- no_http2
 --- config
     location /sub {
         content_by_lua '
diff --git a/t/016-resp-header.t b/t/016-resp-header.t
index 6cf699d88e..b30090812c 100644
--- a/t/016-resp-header.t
+++ b/t/016-resp-header.t
@@ -298,6 +298,7 @@ Fooy: cony1, cony2
 
 
 === TEST 15: set header after ngx.print
+--- no_http2
 --- config
     location /lua {
         default_type "text/plain";
diff --git a/t/020-subrequest.t b/t/020-subrequest.t
index 37914be061..e91f3f6253 100644
--- a/t/020-subrequest.t
+++ b/t/020-subrequest.t
@@ -1198,6 +1198,7 @@ body:
 
 
 === TEST 43: subrequests with an output body filter returning NGX_ERROR
+--- no_http2
 --- config
     location /sub {
         echo hello world;
diff --git a/t/023-rewrite/exit.t b/t/023-rewrite/exit.t
index 9add80441c..7f01717eb6 100644
--- a/t/023-rewrite/exit.t
+++ b/t/023-rewrite/exit.t
@@ -120,6 +120,7 @@ GET /api?user=agentz
 
 
 === TEST 6: working with ngx_auth_request (simplest form, w/o ngx_memc)
+--- no_http2
 --- http_config eval
 "
     lua_package_cpath '$::LuaCpath';
@@ -192,6 +193,7 @@ Logged in 56
 
 
 === TEST 7: working with ngx_auth_request (simplest form)
+--- no_http2
 --- http_config eval
 "
     lua_package_cpath '$::LuaCpath';
@@ -264,6 +266,7 @@ Logged in 56
 
 
 === TEST 8: working with ngx_auth_request
+--- no_http2
 --- http_config eval
 "
     lua_package_cpath '$::LuaCpath';
diff --git a/t/024-access/exit.t b/t/024-access/exit.t
index b77778213a..661ee2d8bc 100644
--- a/t/024-access/exit.t
+++ b/t/024-access/exit.t
@@ -114,6 +114,7 @@ GET /api?user=agentz
 
 
 === TEST 6: working with ngx_auth_request (simplest form, w/o ngx_memc)
+--- no_http2
 --- http_config eval
 "
     lua_package_cpath '$::LuaCpath';
@@ -182,6 +183,7 @@ Logged in 56
 
 
 === TEST 7: working with ngx_auth_request (simplest form)
+--- no_http2
 --- http_config eval
 "
     lua_package_cpath '$::LuaCpath';
@@ -249,6 +251,7 @@ Logged in 56
 
 
 === TEST 8: working with ngx_auth_request
+--- no_http2
 --- http_config eval
 "
     lua_package_cpath '$::LuaCpath';
diff --git a/t/026-mysql.t b/t/026-mysql.t
index 02e14b9382..e7ab170600 100644
--- a/t/026-mysql.t
+++ b/t/026-mysql.t
@@ -16,6 +16,7 @@ run_tests();
 __DATA__
 
 === TEST 1: when mysql query timed out, kill that query by Lua
+--- no_http2
 --- http_config
     upstream backend {
         drizzle_server 127.0.0.1:$TEST_NGINX_MYSQL_PORT protocol=mysql
diff --git a/t/033-ctx.t b/t/033-ctx.t
index 782a0fab6e..77bd15f8c1 100644
--- a/t/033-ctx.t
+++ b/t/033-ctx.t
@@ -279,7 +279,7 @@ GET /t
 --- error_log
 ngx.ctx = 32
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
diff --git a/t/041-header-filter.t b/t/041-header-filter.t
index 23fdac02cd..f5be379885 100644
--- a/t/041-header-filter.t
+++ b/t/041-header-filter.t
@@ -125,7 +125,7 @@ GET /read
 --- error_code
 --- response_body
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -468,7 +468,7 @@ failed to run header_filter_by_lua*: header_filter_by_lua(nginx.conf:47):2: Some
 --- no_error_log
 [alert]
 --- curl_error eval
-qr/curl: \(56\) Failure when receiving data from the peer|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(52\) Empty reply from server|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(56\) Failure when receiving data from the peer|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(52\) Empty reply from server|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -492,7 +492,7 @@ failed to run header_filter_by_lua*: unknown reason
 --- no_error_log
 [alert]
 --- curl_error eval
-qr/curl: \(56\) Failure when receiving data from the peer|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(52\) Empty reply from server|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(56\) Failure when receiving data from the peer|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(52\) Empty reply from server|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -508,7 +508,7 @@ GET /lua
 --- error_log
 API disabled in the context of header_filter_by_lua*
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -524,7 +524,7 @@ GET /lua
 --- error_log
 API disabled in the context of header_filter_by_lua*
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -540,7 +540,7 @@ GET /lua
 --- error_log
 API disabled in the context of header_filter_by_lua*
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -556,7 +556,7 @@ GET /lua
 --- error_log
 API disabled in the context of header_filter_by_lua*
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -572,7 +572,7 @@ GET /lua
 --- error_log
 API disabled in the context of header_filter_by_lua*
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -592,7 +592,7 @@ GET /lua
 --- error_log
 API disabled in the context of header_filter_by_lua*
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -612,7 +612,7 @@ GET /lua
 --- error_log
 API disabled in the context of header_filter_by_lua*
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -628,7 +628,7 @@ GET /lua
 --- error_log
 API disabled in the context of header_filter_by_lua*
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -644,7 +644,7 @@ GET /lua
 --- error_log
 API disabled in the context of header_filter_by_lua*
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -660,7 +660,7 @@ GET /lua
 --- error_log
 API disabled in the context of header_filter_by_lua*
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -694,7 +694,7 @@ GET /lua
 --- error_log eval
 qr/API disabled in the context of header_filter_by_lua\*|http3 requests are not supported without content-length header/ms
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -718,7 +718,7 @@ if (defined $ENV{TEST_NGINX_USE_HTTP3}) {
 
 $err_log;
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -734,7 +734,7 @@ GET /lua
 --- error_log
 API disabled in the context of header_filter_by_lua*
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -750,7 +750,7 @@ GET /lua
 --- error_log
 API disabled in the context of header_filter_by_lua*
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -799,7 +799,7 @@ in function 'error'
 in function 'bar'
 in function 'foo'
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -819,7 +819,7 @@ GET /lua?a=1&b=2
 --- error_log eval
 qr/failed to load external Lua file ".*?test2\.lua": cannot open .*? No such file or directory/
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
diff --git a/t/068-socket-keepalive.t b/t/068-socket-keepalive.t
index 626b441678..84481652ef 100644
--- a/t/068-socket-keepalive.t
+++ b/t/068-socket-keepalive.t
@@ -1384,6 +1384,7 @@ bad argument #3 to 'connect' (bad "pool" option type: boolean)
 
 
 === TEST 23: clear the redis store
+--- no_http2
 --- config
     location /t {
         redis2_query flushall;
diff --git a/t/091-coroutine.t b/t/091-coroutine.t
index bfbdb38937..16930ed3c0 100644
--- a/t/091-coroutine.t
+++ b/t/091-coroutine.t
@@ -763,7 +763,7 @@ GET /lua
 --- error_log
 API disabled in the context of header_filter_by_lua*
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
@@ -1423,6 +1423,7 @@ GET /t
 
 
 === TEST 35: coroutine.wrap runtime errors do not log errors
+--- no_http2
 --- config
     location = /t {
         content_by_lua_block {
@@ -1700,7 +1701,7 @@ GET /t
     "in function 'co'"
 ]
 --- curl_error eval
-qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 0 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
+qr/curl: \(52\) Empty reply from server|curl: \(92\) HTTP\/2 stream 1 was not closed cleanly|curl: \(95\) HTTP\/3 stream 0 reset by server/
 
 
 
diff --git a/t/094-uthread-exit.t b/t/094-uthread-exit.t
index 0194e44b31..5015b5e762 100644
--- a/t/094-uthread-exit.t
+++ b/t/094-uthread-exit.t
@@ -1313,6 +1313,7 @@ attempt to abort with pending subrequests
 
 
 === TEST 16: exit in entry thread (user thread is still pending on ngx.location.capture_multi), without pending output
+--- no_http2
 --- config
     location /lua {
         client_body_timeout 12000ms;
@@ -1407,6 +1408,7 @@ qr#curl: \(52\) Empty reply from server|curl: \(95\) HTTP/3 stream 0 reset by se
 
 
 === TEST 17: exit(444) in user thread (entry thread is still pending on ngx.location.capture), with pending output
+--- no_http2
 --- config
     location /lua {
         client_body_timeout 12000ms;
@@ -1492,6 +1494,7 @@ qr#curl: \(52\) Empty reply from server|curl: \(95\) HTTP/3 stream 0 reset by se
 
 
 === TEST 18: exit(408) in user thread (entry thread is still pending on ngx.location.capture), with pending output
+--- no_http2
 --- config
     location /lua {
         client_body_timeout 12000ms;
diff --git a/t/095-uthread-exec.t b/t/095-uthread-exec.t
index 4cd121da1e..9ef6356090 100644
--- a/t/095-uthread-exec.t
+++ b/t/095-uthread-exec.t
@@ -344,6 +344,7 @@ attempt to abort with pending subrequests
 
 
 === TEST 6: exec in entry thread (user thread is still pending on ngx.location.capture), without pending output
+--- no_http2
 --- config
     location /lua {
         client_body_timeout 12000ms;
diff --git a/t/096-uthread-redirect.t b/t/096-uthread-redirect.t
index 62909b944c..5df5ecfb09 100644
--- a/t/096-uthread-redirect.t
+++ b/t/096-uthread-redirect.t
@@ -190,6 +190,7 @@ free request
 
 
 === TEST 3: ngx.redirect() in entry thread (user thread is still pending on ngx.location.capture_multi), without pending output
+--- no_http2
 --- config
     location /lua {
         client_body_timeout 12000ms;
diff --git a/t/138-balancer.t b/t/138-balancer.t
index 41be75fcdc..30a33e63d0 100644
--- a/t/138-balancer.t
+++ b/t/138-balancer.t
@@ -41,9 +41,6 @@ __DATA__
 '[lua] balancer_by_lua(nginx.conf:27):2: hello from balancer by lua! while connecting to upstream,',
 qr{\[crit\] .*? connect\(\) to 0\.0\.0\.1:80 failed .*?, upstream: "http://0\.0\.0\.1:80/t"},
 ]
---- no_error_log
-[warn]
-
 
 
 === TEST 2: exit 403
@@ -95,8 +92,6 @@ qr{\[crit\] .*? connect\(\) to 0\.0\.0\.1:80 failed .*?, upstream: "http://0\.0\
 '[lua] balancer_by_lua(nginx.conf:27):2: hello from balancer by lua! while connecting to upstream,',
 qr{\[crit\] .*? connect\(\) to 0\.0\.0\.1:80 failed .*?, upstream: "http://0\.0\.0\.1:80/t"},
 ]
---- no_error_log
-[warn]
 
 
 
@@ -125,8 +120,6 @@ qr{\[crit\] .*? connect\(\) to 0\.0\.0\.1:80 failed .*?, upstream: "http://0\.0\
 "2: variable foo = 33",
 qr/\[crit\] .* connect\(\) .*? failed/,
 ]
---- no_error_log
-[warn]
 
 
 
@@ -153,8 +146,6 @@ Foo: bar
 "header foo: bar",
 qr/\[crit\] .* connect\(\) .*? failed/,
 ]
---- no_error_log
-[warn]
 
 
 
@@ -180,12 +171,11 @@ Foo: bar
 ["arg foo: bar",
 qr/\[crit\] .* connect\(\) .*? failed/,
 ]
---- no_error_log
-[warn]
 
 
 
 === TEST 7: ngx.req.get_method() works
+--- no_http2
 --- http_config
     upstream backend {
         server 0.0.0.1;
@@ -208,8 +198,6 @@ Foo: bar
 "method: GET",
 qr/\[crit\] .* connect\(\) .*? failed/,
 ]
---- no_error_log
-[warn]
 
 
 
@@ -235,9 +223,6 @@ print("hello from balancer by lua!")
 '[lua] a.lua:1: hello from balancer by lua! while connecting to upstream,',
 qr{\[crit\] .*? connect\(\) to 0\.0\.0\.1:80 failed .*?, upstream: "http://0\.0\.0\.1:80/t"},
 ]
---- no_error_log
-[warn]
-
 
 
 === TEST 9: cosockets are disabled
@@ -431,8 +416,6 @@ ctx counter: nil
 '[lua] balancer_by_lua(nginx.conf:27):2: hello from balancer by lua! while connecting to upstream,',
 qr{\[crit\] .*? connect\(\) to 0\.0\.0\.1:80 failed .*?, upstream: "http://0\.0\.0\.1:80/t"},
 ]
---- no_error_log
-[warn]
 
 
 
@@ -589,8 +572,6 @@ upstream sent more data than specified in "Content-Length" header while reading
 --- error_code: 500
 --- error_log eval
  "failed to load inlined Lua code: balancer_by_lua(nginx.conf:27):3: ')' expected (to close '(' at line 2) near '<eof>'",
---- no_error_log
-[warn]
 
 
 
diff --git a/t/143-ssl-session-fetch.t b/t/143-ssl-session-fetch.t
index b8ca095aa0..72bb3268ad 100644
--- a/t/143-ssl-session-fetch.t
+++ b/t/143-ssl-session-fetch.t
@@ -1319,7 +1319,6 @@ connected: 1
 ssl handshake: cdata
 close: 1 nil
 --- no_error_log
-[warn]
 [error]
 [alert]
 [emerg]