diff --git a/lib/http.c b/lib/http.c
index cd656cc8b5..0ce3b25bc3 100644
--- a/lib/http.c
+++ b/lib/http.c
@@ -107,9 +107,6 @@ static CURLcode http_header(struct Curl_easy *data,
                             const char *hd, size_t hdlen);
 static CURLcode http_range(struct Curl_easy *data,
                            Curl_HttpReq httpreq);
-static CURLcode http_req_complete(struct Curl_easy *data,
-                                  struct dynbuf *r, int httpversion,
-                                  Curl_HttpReq httpreq);
 static CURLcode http_req_set_TE(struct Curl_easy *data,
                                 struct dynbuf *req,
                                 int httpversion);
@@ -1704,9 +1701,8 @@ CURLcode Curl_add_custom_headers(struct Curl_easy *data,
                  we will force length zero then */
               curlx_str_casecompare(&name, "Content-Length"))
         ;
-      else if(data->state.http_connection_hd_added &&
-              /* when Connection: header has already been added */
-              curlx_str_casecompare(&name, "Connection"))
+      else if(curlx_str_casecompare(&name, "Connection"))
+        /* Normal Connection: header generation takes care of this */
         ;
       else if((httpversion >= 20) &&
               curlx_str_casecompare(&name, "Transfer-Encoding"))
@@ -2320,9 +2316,10 @@ static CURLcode addexpect(struct Curl_easy *data, struct dynbuf *r,
   return CURLE_OK;
 }
 
-static CURLcode http_req_complete(struct Curl_easy *data,
-                                  struct dynbuf *r, int httpversion,
-                                  Curl_HttpReq httpreq)
+static CURLcode http_add_content_hds(struct Curl_easy *data,
+                                     struct dynbuf *r,
+                                     int httpversion,
+                                     Curl_HttpReq httpreq)
 {
   CURLcode result = CURLE_OK;
   curl_off_t req_clen;
@@ -2390,19 +2387,11 @@ static CURLcode http_req_complete(struct Curl_easy *data,
     break;
   }
 
-  /* end of headers */
-  result = curlx_dyn_addn(r, STRCONST("\r\n"));
-  if(!result) {
-    Curl_pgrsSetUploadSize(data, req_clen);
-    if(announced_exp100)
-      result = http_exp100_add_reader(data);
-  }
+  Curl_pgrsSetUploadSize(data, req_clen);
+  if(announced_exp100)
+    result = http_exp100_add_reader(data);
 
 out:
-  if(!result) {
-    /* setup variables for the upcoming transfer */
-    Curl_xfer_setup_sendrecv(data, FIRSTSOCKET, -1);
-  }
   return result;
 }
 
@@ -2645,6 +2634,38 @@ static CURLcode http_check_new_conn(struct Curl_easy *data)
   return CURLE_OK;
 }
 
+static CURLcode http_add_connection_hd(struct Curl_easy *data,
+                                       struct dynbuf *req)
+{
+  char *custom = Curl_checkheaders(data, STRCONST("Connection"));
+  char *custom_val = custom ? Curl_copy_header_value(custom) : NULL;
+  const char *sep = (custom_val && *custom_val) ? ", " : "Connection: ";
+  CURLcode result = CURLE_OK;
+  size_t rlen = curlx_dyn_len(req);
+
+  if(custom && !custom_val)
+    return CURLE_OUT_OF_MEMORY;
+
+  if(custom_val && *custom_val)
+    result = curlx_dyn_addf(req, "Connection: %s", custom_val);
+  if(!result && data->state.http_hd_te) {
+    result = curlx_dyn_addf(req, "%s%s", sep, "TE");
+    sep = ", ";
+  }
+  if(!result && data->state.http_hd_upgrade) {
+    result = curlx_dyn_addf(req, "%s%s", sep, "Upgrade");
+    sep = ", ";
+  }
+  if(!result && data->state.http_hd_h2_settings) {
+    result = curlx_dyn_addf(req, "%s%s", sep, "HTTP2-Settings");
+  }
+  if(rlen < curlx_dyn_len(req))
+    result = curlx_dyn_addn(req, STRCONST("\r\n"));
+
+  free(custom_val);
+  return result;
+}
+
 /* Header identifier in order we send them by default */
 typedef enum {
   H1_HD_REQUEST,
@@ -2668,19 +2689,19 @@ typedef enum {
 #endif
   H1_HD_UPGRADE,
   H1_HD_COOKIES,
-#ifndef CURL_DISABLE_WEBSOCKETS
-  H1_HD_WEBSOCKET,
-#endif
   H1_HD_CONDITIONALS,
   H1_HD_CUSTOM,
-  H1_HD_LAST  /* not a header, just the last enum value for iterating */
+  H1_HD_CONTENT,
+  H1_HD_CONNECTION,
+  H1_HD_LAST  /* the last, empty header line */
 } http_hd_t;
 
 static CURLcode http_add_hd(struct Curl_easy *data,
                             struct dynbuf *req,
                             http_hd_t id,
                             unsigned char httpversion,
-                            const char *method)
+                            const char *method,
+                            Curl_HttpReq httpreq)
 {
   CURLcode result = CURLE_OK;
   switch(id) {
@@ -2733,26 +2754,8 @@ static CURLcode http_add_hd(struct Curl_easy *data,
 #ifdef HAVE_LIBZ
     if(!Curl_checkheaders(data, STRCONST("TE")) &&
        data->set.http_transfer_encoding) {
-      /* When we are to insert a TE: header in the request, we must also insert
-         TE in a Connection: header, so we need to merge the custom provided
-         Connection: header and prevent the original to get sent. Note that if
-         the user has inserted his/her own TE: header we do not do this magic
-         but then assume that the user will handle it all! */
-      char *cptr = Curl_checkheaders(data, STRCONST("Connection"));
-      if(cptr) {
-        cptr = Curl_copy_header_value(cptr);
-        if(!cptr)
-          return CURLE_OUT_OF_MEMORY;
-      }
-
-      data->state.http_connection_hd_added = TRUE;
-      if(cptr && *cptr)
-        result = curlx_dyn_addf(req, "Connection: %s, TE\r\nTE: gzip\r\n",
-                                cptr);
-      else
-        result = curlx_dyn_add(req, "Connection: TE\r\nTE: gzip\r\n");
-
-      free(cptr);
+      data->state.http_hd_te = TRUE;
+      result = curlx_dyn_add(req, "TE: gzip\r\n");
     }
 #endif
     break;
@@ -2803,19 +2806,16 @@ static CURLcode http_add_hd(struct Curl_easy *data,
          over SSL */
       result = Curl_http2_request_upgrade(req, data);
     }
+#ifndef CURL_DISABLE_WEBSOCKETS
+    if(!result && data->conn->handler->protocol&(CURLPROTO_WS|CURLPROTO_WSS))
+      result = Curl_ws_request(data, req);
+#endif
     break;
 
   case H1_HD_COOKIES:
     result = http_cookies(data, req);
     break;
 
-#ifndef CURL_DISABLE_WEBSOCKETS
-  case H1_HD_WEBSOCKET:
-    if(data->conn->handler->protocol&(CURLPROTO_WS|CURLPROTO_WSS))
-      result = Curl_ws_request(data, req);
-    break;
-#endif
-
   case H1_HD_CONDITIONALS:
     result = Curl_add_timecondition(data, req);
     break;
@@ -2824,8 +2824,17 @@ static CURLcode http_add_hd(struct Curl_easy *data,
     result = Curl_add_custom_headers(data, FALSE, httpversion, req);
     break;
 
-  default:
-    DEBUGASSERT(0);
+  case H1_HD_CONTENT:
+    result = http_add_content_hds(data, req, httpversion, httpreq);
+    break;
+
+  case H1_HD_CONNECTION: {
+    result = http_add_connection_hd(data, req);
+    break;
+  }
+
+  case H1_HD_LAST:
+    result = curlx_dyn_addn(req, STRCONST("\r\n"));
     break;
   }
   return result;
@@ -2867,7 +2876,10 @@ CURLcode Curl_http(struct Curl_easy *data, bool *done)
   result = Curl_headers_init(data);
   if(result)
     goto out;
-  data->state.http_connection_hd_added = FALSE;
+
+  data->state.http_hd_te = FALSE;
+  data->state.http_hd_upgrade = FALSE;
+  data->state.http_hd_h2_settings = FALSE;
 
   /* what kind of request do we need to send? */
   Curl_http_method(data, &method, &httpreq);
@@ -2904,17 +2916,15 @@ CURLcode Curl_http(struct Curl_easy *data, bool *done)
 
   httpversion = http_request_version(data);
   /* Add request line and all headers to `req` */
-  for(hd_id = 0; hd_id < H1_HD_LAST; ++hd_id) {
-    result = http_add_hd(data, &req, (http_hd_t)hd_id, httpversion, method);
+  for(hd_id = 0; hd_id <= H1_HD_LAST; ++hd_id) {
+    result = http_add_hd(data, &req, (http_hd_t)hd_id,
+                         httpversion, method, httpreq);
     if(result)
       goto out;
   }
 
-  /* Add any final headers, including the last, empty line */
-  result = http_req_complete(data, &req, httpversion, httpreq);
-  if(result)
-    goto out;
-
+  /* setup variables for the upcoming transfer and send */
+  Curl_xfer_setup_sendrecv(data, FIRSTSOCKET, -1);
   result = Curl_req_send(data, &req, httpversion);
 
   if((httpversion >= 20) && data->req.upload_chunky)
diff --git a/lib/http2.c b/lib/http2.c
index 7c95c2ff7e..e2cdc9181f 100644
--- a/lib/http2.c
+++ b/lib/http2.c
@@ -1820,8 +1820,9 @@ CURLcode Curl_http2_request_upgrade(struct dynbuf *req,
     return result;
   }
 
+  data->state.http_hd_upgrade = TRUE;
+  data->state.http_hd_h2_settings = TRUE;
   result = curlx_dyn_addf(req,
-                          "Connection: Upgrade, HTTP2-Settings\r\n"
                           "Upgrade: %s\r\n"
                           "HTTP2-Settings: %s\r\n",
                           NGHTTP2_CLEARTEXT_PROTO_VERSION_ID, base64);
diff --git a/lib/http_proxy.c b/lib/http_proxy.c
index 5b1d118584..2d742856ce 100644
--- a/lib/http_proxy.c
+++ b/lib/http_proxy.c
@@ -162,10 +162,6 @@ static CURLcode dynhds_add_custom(struct Curl_easy *data,
                  we will force length zero then */
               hd_name_eq(name, namelen, STRCONST("Content-Length:")))
         ;
-      else if(data->state.http_connection_hd_added &&
-              /* when Connection: header has already been added */
-              hd_name_eq(name, namelen, STRCONST("Connection:")))
-        ;
       else if((httpversion >= 20) &&
               hd_name_eq(name, namelen, STRCONST("Transfer-Encoding:")))
         /* HTTP/2 and HTTP/3 do not support chunked requests */
diff --git a/lib/urldata.h b/lib/urldata.h
index b5b1209d3f..cf181af641 100644
--- a/lib/urldata.h
+++ b/lib/urldata.h
@@ -1177,7 +1177,11 @@ struct UrlState {
                     internal use and the user does not have ownership of the
                     handle. */
   BIT(http_ignorecustom); /* ignore custom method from now */
-  BIT(http_connection_hd_added); /* 'Connection: ' header already added */
+#ifndef CURL_DISABLE_HTTP
+  BIT(http_hd_te); /* Added HTTP header TE: */
+  BIT(http_hd_upgrade); /* Added HTTP header Upgrade: */
+  BIT(http_hd_h2_settings); /* Added HTTP header H2Settings: */
+#endif
 };
 
 /*
diff --git a/lib/ws.c b/lib/ws.c
index b6434b0b80..6070cd6d0d 100644
--- a/lib/ws.c
+++ b/lib/ws.c
@@ -1023,11 +1023,6 @@ CURLcode Curl_ws_request(struct Curl_easy *data, struct dynbuf *req)
          MUST include the "websocket" keyword. */
       "Upgrade", "websocket"
     },
-    {
-      /* The request MUST contain a |Connection| header field whose value
-         MUST include the "Upgrade" token. */
-      "Connection", "Upgrade",
-    },
     {
       /* The request MUST include a header field with the name
          |Sec-WebSocket-Version|. The value of this header field MUST be
@@ -1043,7 +1038,7 @@ CURLcode Curl_ws_request(struct Curl_easy *data, struct dynbuf *req)
       "Sec-WebSocket-Key", NULL,
     }
   };
-  heads[3].val = &keyval[0];
+  heads[2].val = &keyval[0];
 
   /* 16 bytes random */
   result = Curl_rand(data, (unsigned char *)rand, sizeof(rand));
@@ -1065,6 +1060,7 @@ CURLcode Curl_ws_request(struct Curl_easy *data, struct dynbuf *req)
                               heads[i].val);
     }
   }
+  data->state.http_hd_upgrade = TRUE;
   k->upgr101 = UPGR101_WS;
   return result;
 }
diff --git a/tests/data/test1122 b/tests/data/test1122
index 073c59acbf..d0ce3ffaf0 100644
--- a/tests/data/test1122
+++ b/tests/data/test1122
@@ -66,8 +66,8 @@ GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Connection: TE
 TE: gzip
+Connection: TE
 
 </protocol>
 </verify>
diff --git a/tests/data/test1123 b/tests/data/test1123
index 08320aa599..a01aae69be 100644
--- a/tests/data/test1123
+++ b/tests/data/test1123
@@ -176,8 +176,8 @@ GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Connection: TE
 TE: gzip
+Connection: TE
 
 </protocol>
 </verify>
diff --git a/tests/data/test1124 b/tests/data/test1124
index ee969cda0a..fdc172398f 100644
--- a/tests/data/test1124
+++ b/tests/data/test1124
@@ -67,8 +67,8 @@ GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Connection: TE
 TE: gzip
+Connection: TE
 
 </protocol>
 </verify>
diff --git a/tests/data/test1125 b/tests/data/test1125
index 248432f3ce..3b4d58b2e6 100644
--- a/tests/data/test1125
+++ b/tests/data/test1125
@@ -66,8 +66,8 @@ GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Connection: close, TE
 TE: gzip
+Connection: close, TE
 
 </protocol>
 </verify>
diff --git a/tests/data/test1170 b/tests/data/test1170
index f3ade56b7e..d6271714bd 100644
--- a/tests/data/test1170
+++ b/tests/data/test1170
@@ -66,8 +66,8 @@ GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Connection: TE
 TE: gzip
+Connection: TE
 
 </protocol>
 </verify>
diff --git a/tests/data/test1171 b/tests/data/test1171
index 14d660176b..486aadb94b 100644
--- a/tests/data/test1171
+++ b/tests/data/test1171
@@ -66,8 +66,8 @@ GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Connection: TE
 TE: gzip
+Connection: TE
 
 </protocol>
 </verify>
diff --git a/tests/data/test1277 b/tests/data/test1277
index 7b163a47e7..52a0f675a2 100644
--- a/tests/data/test1277
+++ b/tests/data/test1277
@@ -183,9 +183,9 @@ GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Connection: TE
 TE: gzip
 Accept-Encoding: xxx
+Connection: TE
 
 </protocol>
 </verify>
diff --git a/tests/data/test1546 b/tests/data/test1546
index 0ec7093f71..b83b7ee95f 100644
--- a/tests/data/test1546
+++ b/tests/data/test1546
@@ -52,8 +52,8 @@ GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Connection: TE
 TE: gzip
+Connection: TE
 
 </protocol>
 <errorcode>
diff --git a/tests/data/test1704 b/tests/data/test1704
index 0401f796b4..324551a068 100644
--- a/tests/data/test1704
+++ b/tests/data/test1704
@@ -52,9 +52,9 @@ GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Connection: Upgrade, HTTP2-Settings
 Upgrade: h2c
 HTTP2-Settings: AAMAAABkAAQAAQAAAAIAAAAA
+Connection: Upgrade, HTTP2-Settings
 
 </protocol>
 
diff --git a/tests/data/test1800 b/tests/data/test1800
index b1fd8021a6..222437e8e1 100644
--- a/tests/data/test1800
+++ b/tests/data/test1800
@@ -47,9 +47,9 @@ GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Connection: Upgrade, HTTP2-Settings
 Upgrade: %H2CVER
 HTTP2-Settings: AAMAAABkAAQAAQAAAAIAAAAA
+Connection: Upgrade, HTTP2-Settings
 
 </protocol>
 </verify>
diff --git a/tests/data/test2300 b/tests/data/test2300
index 18a38e04d0..8b28774686 100644
--- a/tests/data/test2300
+++ b/tests/data/test2300
@@ -53,9 +53,9 @@ Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
 Upgrade: websocket
-Connection: Upgrade
 Sec-WebSocket-Version: 13
 Sec-WebSocket-Key: NDMyMTUzMjE2MzIxNzMyMQ==
+Connection: Upgrade
 
 </protocol>
 <errorcode>
diff --git a/tests/data/test2301 b/tests/data/test2301
index e3cab99f15..1b968c7672 100644
--- a/tests/data/test2301
+++ b/tests/data/test2301
@@ -58,9 +58,9 @@ Host: %HOSTIP:%HTTPPORT
 User-Agent: webbie-sox/3
 Accept: */*
 Upgrade: websocket
-Connection: Upgrade
 Sec-WebSocket-Version: 13
 Sec-WebSocket-Key: NDMyMTUzMjE2MzIxNzMyMQ==
+Connection: Upgrade
 
 %hex[%8a%00]hex%
 </protocol>
diff --git a/tests/data/test2302 b/tests/data/test2302
index b1d11fcf6e..8e2d34877f 100644
--- a/tests/data/test2302
+++ b/tests/data/test2302
@@ -59,9 +59,9 @@ Host: %HOSTIP:%HTTPPORT
 User-Agent: webbie-sox/3
 Accept: */*
 Upgrade: websocket
-Connection: Upgrade
 Sec-WebSocket-Version: 13
 Sec-WebSocket-Key: NDMyMTUzMjE2MzIxNzMyMQ==
+Connection: Upgrade
 
 %hex[%8a%808321]hex%
 </protocol>
diff --git a/tests/data/test2303 b/tests/data/test2303
index d90d23dc9e..8ad45cbeca 100644
--- a/tests/data/test2303
+++ b/tests/data/test2303
@@ -49,9 +49,9 @@ Host: %HOSTIP:%HTTPPORT
 User-Agent: webbie-sox/3
 Accept: */*
 Upgrade: websocket
-Connection: Upgrade
 Sec-WebSocket-Version: 13
 Sec-WebSocket-Key: NDMyMTUzMjE2MzIxNzMyMQ==
+Connection: Upgrade
 
 </protocol>
 # 22 == CURLE_HTTP_RETURNED_ERROR
diff --git a/tests/data/test2304 b/tests/data/test2304
index 21fac7a0f0..8ed75d96a9 100644
--- a/tests/data/test2304
+++ b/tests/data/test2304
@@ -58,9 +58,9 @@ Host: %HOSTIP:%HTTPPORT
 User-Agent: websocket/%TESTNUMBER
 Accept: */*
 Upgrade: websocket
-Connection: Upgrade
 Sec-WebSocket-Version: 13
 Sec-WebSocket-Key: NDMyMTUzMjE2MzIxNzMyMQ==
+Connection: Upgrade
 
 </protocol>
 
diff --git a/tests/data/test387 b/tests/data/test387
index d0e5c95ed4..a6d2ab03fc 100644
--- a/tests/data/test387
+++ b/tests/data/test387
@@ -43,8 +43,8 @@ GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Connection: TE
 TE: gzip
+Connection: TE
 
 </protocol>
 
diff --git a/tests/data/test418 b/tests/data/test418
index 6031b867b8..fa502f1b56 100644
--- a/tests/data/test418
+++ b/tests/data/test418
@@ -51,8 +51,8 @@ GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Connection: TE
 TE: gzip
+Connection: TE
 
 </protocol>