diff --git a/tests/http/test_02_download.py b/tests/http/test_02_download.py
index 47f0417e79..fa2c002091 100644
--- a/tests/http/test_02_download.py
+++ b/tests/http/test_02_download.py
@@ -577,12 +577,10 @@ class TestDownload:
     @pytest.mark.skipif(condition=not Env.have_nghttpx(), reason="no nghttpx")
     @pytest.mark.parametrize("proto", ['http/1.1', 'h2', 'h3'])
     def test_02_32_earlydata(self, env: Env, httpd, nghttpx, proto):
-        if not env.curl_uses_lib('gnutls') and \
-           not env.curl_uses_lib('wolfssl') and \
-           not env.curl_uses_lib('quictls') and \
-           not env.curl_uses_lib('openssl'):
+        if not env.curl_can_early_data():
             pytest.skip('TLS earlydata not implemented')
-        if proto == 'h3' and not env.have_h3():
+        if proto == 'h3' and \
+           (not env.have_h3() or not env.curl_can_h3_early_data()):
             pytest.skip("h3 not supported")
         count = 2
         docname = 'data-10k'
diff --git a/tests/http/test_07_upload.py b/tests/http/test_07_upload.py
index b34d0c2f26..53e5a00a35 100644
--- a/tests/http/test_07_upload.py
+++ b/tests/http/test_07_upload.py
@@ -703,12 +703,10 @@ class TestUpload:
                                        # of 128K.
     ])
     def test_07_70_put_earlydata(self, env: Env, httpd, nghttpx, proto, upload_size, exp_early):
-        if not env.curl_uses_lib('gnutls') and \
-           not env.curl_uses_lib('wolfssl') and \
-           not env.curl_uses_lib('quictls') and \
-           not env.curl_uses_lib('openssl'):
+        if not env.curl_can_early_data():
             pytest.skip('TLS earlydata not implemented')
-        if proto == 'h3' and not env.have_h3():
+        if proto == 'h3' and \
+           (not env.have_h3() or not env.curl_can_h3_early_data()):
             pytest.skip("h3 not supported")
         count = 2
         # we want this test to always connect to nghttpx, since it is
diff --git a/tests/http/test_08_caddy.py b/tests/http/test_08_caddy.py
index 776c0362cb..cd16e0d954 100644
--- a/tests/http/test_08_caddy.py
+++ b/tests/http/test_08_caddy.py
@@ -207,12 +207,10 @@ class TestCaddy:
 
     @pytest.mark.parametrize("proto", ['http/1.1', 'h2', 'h3'])
     def test_08_08_earlydata(self, env: Env, httpd, caddy, proto):
-        if not env.curl_uses_lib('gnutls') and \
-           not env.curl_uses_lib('wolfssl') and \
-           not env.curl_uses_lib('quictls') and \
-           not env.curl_uses_lib('openssl'):
+        if not env.curl_can_early_data():
             pytest.skip('TLS earlydata not implemented')
-        if proto == 'h3' and not env.have_h3():
+        if proto == 'h3' and \
+           (not env.have_h3() or not env.curl_can_h3_early_data()):
             pytest.skip("h3 not supported")
         count = 2
         docname = 'data10k.data'
diff --git a/tests/http/testenv/env.py b/tests/http/testenv/env.py
index 3b13a5c6bf..a4ab7a9801 100644
--- a/tests/http/testenv/env.py
+++ b/tests/http/testenv/env.py
@@ -382,6 +382,18 @@ class Env:
     def curl_is_debug() -> bool:
         return Env.CONFIG.curl_is_debug
 
+    @staticmethod
+    def curl_can_early_data() -> bool:
+        return Env.curl_uses_lib('gnutls') or \
+            Env.curl_uses_lib('wolfssl') or \
+            Env.curl_uses_lib('quictls') or \
+            Env.curl_uses_lib('openssl')
+
+    @staticmethod
+    def curl_can_h3_early_data() -> bool:
+        return Env.curl_can_early_data() and \
+            Env.curl_uses_lib('ngtcp2')
+
     @staticmethod
     def have_h3() -> bool:
         return Env.have_h3_curl() and Env.have_h3_server()