diff --git a/channels/chan_iax2.c b/channels/chan_iax2.c
index 98401fbf9dbd8de501ccd6feb12410f830644d64..c1e3b0f5f3edd735e0b5e0f456912f825a44ecf5 100644
--- a/channels/chan_iax2.c
+++ b/channels/chan_iax2.c
@@ -241,6 +241,7 @@ static int trunkmaxsize = MAX_TRUNKDATA;
 static int authdebug = 1;
 static int autokill = 0;
 static int iaxcompat = 0;
+static int last_authmethod = 0;
 
 static int iaxdefaultdpcache=10 * 60;	/* Cache dialplan entries for 10 minutes by default */
 
@@ -7333,23 +7334,34 @@ static int registry_authrequest(int callno)
 	char challenge[10];
 	const char *peer_name;
 	int res = -1;
+	int sentauthmethod;
 
 	peer_name = ast_strdupa(iaxs[callno]->peer);
 
 	/* SLD: third call to find_peer in registration */
 	ast_mutex_unlock(&iaxsl[callno]);
-	p = find_peer(peer_name, 1);
+	if ((p = find_peer(peer_name, 1))) {
+		last_authmethod = p->authmethods;
+	}
+
 	ast_mutex_lock(&iaxsl[callno]);
 	if (!iaxs[callno])
 		goto return_unref;
-	if (!p) {
+	if (!p && !delayreject) {
 		ast_log(LOG_WARNING, "No such peer '%s'\n", peer_name);
 		goto return_unref;
 	}
 	
 	memset(&ied, 0, sizeof(ied));
-	iax_ie_append_short(&ied, IAX_IE_AUTHMETHODS, p->authmethods);
-	if (p->authmethods & (IAX_AUTH_RSA | IAX_AUTH_MD5)) {
+	/* The selection of which delayed reject is sent may leak information,
+	 * if it sets a static response.  For example, if a host is known to only
+	 * use MD5 authentication, then an RSA response would indicate that the
+	 * peer does not exist, and vice-versa.
+	 * Therefore, we use whatever the last peer used (which may vary over the
+	 * course of a server, which should leak minimal information). */
+	sentauthmethod = p ? p->authmethods : last_authmethod ? last_authmethod : (IAX_AUTH_MD5 | IAX_AUTH_PLAINTEXT);
+	iax_ie_append_short(&ied, IAX_IE_AUTHMETHODS, sentauthmethod);
+	if (sentauthmethod & (IAX_AUTH_RSA | IAX_AUTH_MD5)) {
 		/* Build the challenge */
 		snprintf(challenge, sizeof(challenge), "%d", (int)ast_random());
 		ast_string_field_set(iaxs[callno], challenge, challenge);