diff --git a/lib/c-hyper.c b/lib/c-hyper.c
index 7389210cc8..de09568741 100644
--- a/lib/c-hyper.c
+++ b/lib/c-hyper.c
@@ -904,6 +904,8 @@ CURLcode Curl_http(struct Curl_easy *data, bool *done)
     hyper_clientconn_options_http2(options, 1);
     h2 = TRUE;
   }
+  hyper_clientconn_options_set_preserve_header_case(options, 1);
+  hyper_clientconn_options_set_preserve_header_order(options, 1);
 
   hyper_clientconn_options_exec(options, h->exec);
 
diff --git a/lib/http_proxy.c b/lib/http_proxy.c
index 1aace7844a..863cbbbdce 100644
--- a/lib/http_proxy.c
+++ b/lib/http_proxy.c
@@ -767,6 +767,9 @@ static CURLcode CONNECT(struct Curl_easy *data,
       }
 
       options = hyper_clientconn_options_new();
+      hyper_clientconn_options_set_preserve_header_case(options, 1);
+      hyper_clientconn_options_set_preserve_header_order(options, 1);
+
       if(!options) {
         failf(data, "Couldn't create hyper client options");
         result = CURLE_OUT_OF_MEMORY;
diff --git a/tests/data/DISABLED b/tests/data/DISABLED
index 7d4110461c..efdfeefc82 100644
--- a/tests/data/DISABLED
+++ b/tests/data/DISABLED
@@ -45,8 +45,6 @@
 357
 565
 579
-580
-581
 587
 670
 671