diff --git a/res/res_pjsip_sdp_rtp.c b/res/res_pjsip_sdp_rtp.c
index 43b89a988c..7c7040e35b 100644
--- a/res/res_pjsip_sdp_rtp.c
+++ b/res/res_pjsip_sdp_rtp.c
@@ -1376,8 +1376,8 @@ static int create_outgoing_sdp_stream(struct ast_sip_session *session, struct as
 	attr->name = STR_SENDRECV;
 	media->attr[media->attr_count++] = attr;
 
-	/* If we've got rtcp-mux enabled, just unconditionally offer it in all SDPs */
-	if (session->endpoint->rtcp_mux) {
+	/* If we've got rtcp-mux enabled, add it unless we received an offer without it */
+	if (session->endpoint->rtcp_mux && session_media->remote_rtcp_mux) {
 		attr = pjmedia_sdp_attr_create(pool, "rtcp-mux", NULL);
 		pjmedia_sdp_attr_add(&media->attr_count, media->attr, attr);
 	}
diff --git a/res/res_pjsip_session.c b/res/res_pjsip_session.c
index 8eaeb31a7b..ed637cdd52 100644
--- a/res/res_pjsip_session.c
+++ b/res/res_pjsip_session.c
@@ -1342,6 +1342,7 @@ static int add_session_media(void *obj, void *arg, int flags)
 	}
 	session_media->encryption = session->endpoint->media.rtp.encryption;
 	session_media->remote_ice = session->endpoint->media.rtp.ice_support;
+	session_media->remote_rtcp_mux = session->endpoint->rtcp_mux;
 	session_media->keepalive_sched_id = -1;
 	session_media->timeout_sched_id = -1;
 	/* Safe use of strcpy */