diff --git a/test/functional/configs/merged-local.conf b/test/functional/configs/merged-local.conf
index 963fd1ec0e..8aeb4f4574 100644
--- a/test/functional/configs/merged-local.conf
+++ b/test/functional/configs/merged-local.conf
@@ -40,8 +40,8 @@ external_relay {
       user_map = "{= env.TESTDIR =}/configs/maps/external_relay.user_map";
     }
     EXTERNAL_RELAY_COUNT {
-      # since the relay count is 10, don't make other test cases' Received headers more than 10
-      count = 10;
+      count = 4;
+      priority = 30;
       strategy = "count";
     }
     EXTERNAL_RELAY_HOSTNAME_MAP {
diff --git a/test/functional/messages/received4.eml b/test/functional/messages/received4.eml
index b29f51930b..d34ebb1bef 100644
--- a/test/functional/messages/received4.eml
+++ b/test/functional/messages/received4.eml
@@ -1,9 +1,3 @@
-Received: Padding for
-Received: external_relay
-Received: strategy of header count
-Received: The number of the
-Received: header in other test cases
-Received: should less than TEN
 Received: apparently
 Received: or is it
 Received: from server.chat-met-vreemden.nl (unknown [IPv6:2a01:7c8:aab6:26d:5054:ff:fed1:1da2])