diff --git a/docs/HYPER.md b/docs/HYPER.md
index a0f39696bd..00c85d576a 100644
--- a/docs/HYPER.md
+++ b/docs/HYPER.md
@@ -56,8 +56,9 @@ The hyper backend does not support
 - `CURLOPT_IGNORE_CONTENT_LENGTH`
 - `--raw` and disabling `CURLOPT_HTTP_TRANSFER_DECODING`
 - RTSP
-- hyper is much stricter about what HTTP header contents it allow in requests
+- hyper is much stricter about what HTTP header contents it allows
 - HTTP/0.9
+- HTTP/2 upgrade using HTTP:// URLs. Aka 'h2c'
 
 ## Remaining issues
 
diff --git a/tests/FILEFORMAT.md b/tests/FILEFORMAT.md
index 291c944c96..003df8ea63 100644
--- a/tests/FILEFORMAT.md
+++ b/tests/FILEFORMAT.md
@@ -384,6 +384,7 @@ Features testable here are:
 - `getrlimit`
 - `GnuTLS`
 - `GSS-API`
+- `h2c`
 - `HSTS`
 - `HTTP-auth`
 - `http/2`
diff --git a/tests/data/DISABLED b/tests/data/DISABLED
index 7187ec371d..466dc3208e 100644
--- a/tests/data/DISABLED
+++ b/tests/data/DISABLED
@@ -43,8 +43,6 @@
 265
 266
 357
-358
-359
 565
 579
 580
@@ -60,10 +58,6 @@
 1533
 1540
 1591
-1700
-1701
-1702
-1800
 %endif
 2043
 # Tests that are disabled here for rustls are SUPPOSED to work
diff --git a/tests/data/test1700 b/tests/data/test1700
index 9cf8739285..8b1ef4ae33 100644
--- a/tests/data/test1700
+++ b/tests/data/test1700
@@ -38,6 +38,9 @@ Content-Type: text/html
 #
 # Client-side
 <client>
+<features>
+h2c
+</features>
 <server>
 http
 http/2
diff --git a/tests/data/test1701 b/tests/data/test1701
index c4687d9117..3c1a2bd0b8 100644
--- a/tests/data/test1701
+++ b/tests/data/test1701
@@ -29,6 +29,9 @@ Funny-head: yesyes
 #
 # Client-side
 <client>
+<features>
+h2c
+</features>
 <server>
 http
 http/2
diff --git a/tests/data/test1702 b/tests/data/test1702
index b679c7bca1..1da9bc6b58 100644
--- a/tests/data/test1702
+++ b/tests/data/test1702
@@ -28,6 +28,9 @@ Funny-head: yesyes
 #
 # Client-side
 <client>
+<features>
+h2c
+</features>
 <server>
 http
 http/2
diff --git a/tests/data/test1800 b/tests/data/test1800
index 85e247c3cb..d7cc73af41 100644
--- a/tests/data/test1800
+++ b/tests/data/test1800
@@ -23,6 +23,9 @@ Content-Type: text/html
 
 # Client-side
 <client>
+<features>
+h2c
+</features>
 <server>
 http
 </server>
diff --git a/tests/data/test358 b/tests/data/test358
index d1ddc1b9e7..8b4f660624 100644
--- a/tests/data/test358
+++ b/tests/data/test358
@@ -30,6 +30,7 @@ Alt-Svc: h2=":%HTTP2PORT", ma=315360000; persist=0
 <features>
 alt-svc
 debug
+h2c
 </features>
 <server>
 http
diff --git a/tests/data/test359 b/tests/data/test359
index c1b1cb86c5..a5ba4e3ae0 100644
--- a/tests/data/test359
+++ b/tests/data/test359
@@ -30,6 +30,7 @@ Alt-Svc: h2=":%HTTP2PORT", ma=315360000; persist=0
 <features>
 alt-svc
 debug
+h2c
 </features>
 <server>
 https
diff --git a/tests/runtests.pl b/tests/runtests.pl
index 8b8d6d80b3..21fcf66752 100755
--- a/tests/runtests.pl
+++ b/tests/runtests.pl
@@ -256,6 +256,7 @@ my $has_spnego;     # set if libcurl is built with SPNEGO support
 my $has_charconv;   # set if libcurl is built with CharConv support
 my $has_tls_srp;    # set if libcurl is built with TLS-SRP support
 my $has_http2;      # set if libcurl is built with HTTP2 support
+my $has_h2c;        # set if libcurl is built with h2c support
 my $has_httpsproxy; # set if libcurl is built with HTTPS-proxy support
 my $has_crypto;     # set if libcurl is built with cryptographic support
 my $has_cares;      # set if built with c-ares
@@ -2864,38 +2865,37 @@ sub compare {
 }
 
 sub setupfeatures {
-    $feature{"hyper"} = $has_hyper;
-    $feature{"c-ares"} = $has_cares;
     $feature{"alt-svc"} = $has_altsvc;
-    $feature{"HSTS"} = $has_hsts;
     $feature{"brotli"} = $has_brotli;
+    $feature{"c-ares"} = $has_cares;
     $feature{"crypto"} = $has_crypto;
     $feature{"debug"} = $debug_build;
     $feature{"getrlimit"} = $has_getrlimit;
     $feature{"GnuTLS"} = $has_gnutls;
     $feature{"GSS-API"} = $has_gssapi;
+    $feature{"h2c"} = $has_h2c;
+    $feature{"HSTS"} = $has_hsts;
     $feature{"http/2"} = $has_http2;
     $feature{"https-proxy"} = $has_httpsproxy;
+    $feature{"hyper"} = $has_hyper;
     $feature{"idn"} = $has_idn;
     $feature{"ipv6"} = $has_ipv6;
     $feature{"Kerberos"} = $has_kerberos;
     $feature{"large_file"} = $has_largefile;
     $feature{"ld_preload"} = ($has_ldpreload && !$debug_build);
-    $feature{"libz"} = $has_libz;
-    $feature{"libssh2"} = $has_libssh2;
     $feature{"libssh"} = $has_libssh;
-    $feature{"oldlibssh"} = $has_oldlibssh;
-    $feature{"rustls"} = $has_rustls;
-    $feature{"wolfssh"} = $has_wolfssh;
-    $feature{"wolfssl"} = $has_wolfssl;
+    $feature{"libssh2"} = $has_libssh2;
+    $feature{"libz"} = $has_libz;
     $feature{"manual"} = $has_manual;
     $feature{"MinGW"} = $has_mingw;
     $feature{"MultiSSL"} = $has_multissl;
     $feature{"NSS"} = $has_nss;
     $feature{"NTLM"} = $has_ntlm;
     $feature{"NTLM_WB"} = $has_ntlm_wb;
+    $feature{"oldlibssh"} = $has_oldlibssh;
     $feature{"OpenSSL"} = $has_openssl || $has_libressl || $has_boringssl;
     $feature{"PSL"} = $has_psl;
+    $feature{"rustls"} = $has_rustls;
     $feature{"Schannel"} = $has_schannel;
     $feature{"sectransp"} = $has_sectransp;
     $feature{"SPNEGO"} = $has_spnego;
@@ -2909,6 +2909,8 @@ sub setupfeatures {
     $feature{"unittest"} = $debug_build;
     $feature{"unix-sockets"} = $has_unix;
     $feature{"win32"} = $has_win32;
+    $feature{"wolfssh"} = $has_wolfssh;
+    $feature{"wolfssl"} = $has_wolfssl;
     $feature{"zstd"} = $has_zstd;
 
     # make each protocol an enabled "feature"
@@ -3040,6 +3042,10 @@ sub checksystem {
            if ($libcurl =~ /Hyper/i) {
                $has_hyper=1;
            }
+            if ($libcurl =~ /nghttp2/i) {
+                # nghttp2 supports h2c, hyper does not
+                $has_h2c=1;
+            }
             if ($libcurl =~ /libssh2/i) {
                 $has_libssh2=1;
             }