diff --git a/lib/roles/http/server/server.c b/lib/roles/http/server/server.c
index 499a4e3db..49ff31fec 100644
--- a/lib/roles/http/server/server.c
+++ b/lib/roles/http/server/server.c
@@ -2986,6 +2986,9 @@ int lws_serve_http_file_fragment(struct lws *wsi)
 	unsigned char *p, *pstart;
 #if defined(LWS_WITH_RANGES)
 	unsigned char finished = 0;
+#endif
+#if defined(LWS_ROLE_H2)
+	struct lws *nwsi;
 #endif
 	int n, m;
 
@@ -3067,8 +3070,20 @@ int lws_serve_http_file_fragment(struct lws *wsi)
 		}
 #endif
 
-		poss = context->pt_serv_buf_size - (unsigned int)n -
-				LWS_H2_FRAME_HEADER_LENGTH;
+		poss = context->pt_serv_buf_size;
+
+#if defined(LWS_ROLE_H2)
+		/*
+		 * If it's h2, restrict any lump that we are sending to the
+		 * max h2 frame size the peer indicated he could handle in
+		 * his SETTINGS
+		 */
+		nwsi = lws_get_network_wsi(wsi);
+		if (nwsi->h2.h2n &&
+		    poss > (lws_filepos_t)nwsi->h2.h2n->peer_set.s[H2SET_MAX_FRAME_SIZE])
+			poss = (lws_filepos_t)nwsi->h2.h2n->peer_set.s[H2SET_MAX_FRAME_SIZE];
+#endif
+		poss = poss - (lws_filepos_t)(n + LWS_H2_FRAME_HEADER_LENGTH);
 
 		if (wsi->http.tx_content_length)
 			if (poss > wsi->http.tx_content_remain)