diff --git a/dh.c b/dh.c
index 1e5388d7f..4c639acc3 100644
--- a/dh.c
+++ b/dh.c
@@ -1,4 +1,4 @@
-/* $OpenBSD: dh.c,v 1.56 2015/03/26 06:59:28 djm Exp $ */
+/* $OpenBSD: dh.c,v 1.57 2015/05/27 23:39:18 dtucker Exp $ */
 /*
  * Copyright (c) 2000 Niels Provos.  All rights reserved.
  *
@@ -155,7 +155,7 @@ choose_dh(int min, int wantbits, int max)
 	    (f = fopen(_PATH_DH_PRIMES, "r")) == NULL) {
 		logit("WARNING: %s does not exist, using fixed modulus",
 		    _PATH_DH_MODULI);
-		return (dh_new_group14());
+		return (dh_new_group_fallback(max));
 	}
 
 	linenum = 0;
@@ -183,7 +183,7 @@ choose_dh(int min, int wantbits, int max)
 	if (bestcount == 0) {
 		fclose(f);
 		logit("WARNING: no suitable primes in %s", _PATH_DH_PRIMES);
-		return (dh_new_group14());
+		return (dh_new_group_fallback(max));
 	}
 
 	linenum = 0;
@@ -204,7 +204,7 @@ choose_dh(int min, int wantbits, int max)
 	if (linenum != which+1) {
 		logit("WARNING: line %d disappeared in %s, giving up",
 		    which, _PATH_DH_PRIMES);
-		return (dh_new_group14());
+		return (dh_new_group_fallback(max));
 	}
 
 	return (dh_new_group(dhg.g, dhg.p));
@@ -338,6 +338,45 @@ dh_new_group14(void)
 	return (dh_new_group_asc(gen, group14));
 }
 
+/*
+ * 4k bit fallback group used by DH-GEX if moduli file cannot be read.
+ * Source: MODP group 16 from RFC3526.
+ */
+DH *
+dh_new_group_fallback(int max)
+{
+	static char *gen = "2", *group16 =
+	    "FFFFFFFF" "FFFFFFFF" "C90FDAA2" "2168C234" "C4C6628B" "80DC1CD1"
+	    "29024E08" "8A67CC74" "020BBEA6" "3B139B22" "514A0879" "8E3404DD"
+	    "EF9519B3" "CD3A431B" "302B0A6D" "F25F1437" "4FE1356D" "6D51C245"
+	    "E485B576" "625E7EC6" "F44C42E9" "A637ED6B" "0BFF5CB6" "F406B7ED"
+	    "EE386BFB" "5A899FA5" "AE9F2411" "7C4B1FE6" "49286651" "ECE45B3D"
+	    "C2007CB8" "A163BF05" "98DA4836" "1C55D39A" "69163FA8" "FD24CF5F"
+	    "83655D23" "DCA3AD96" "1C62F356" "208552BB" "9ED52907" "7096966D"
+	    "670C354E" "4ABC9804" "F1746C08" "CA18217C" "32905E46" "2E36CE3B"
+	    "E39E772C" "180E8603" "9B2783A2" "EC07A28F" "B5C55DF0" "6F4C52C9"
+	    "DE2BCBF6" "95581718" "3995497C" "EA956AE5" "15D22618" "98FA0510"
+	    "15728E5A" "8AAAC42D" "AD33170D" "04507A33" "A85521AB" "DF1CBA64"
+	    "ECFB8504" "58DBEF0A" "8AEA7157" "5D060C7D" "B3970F85" "A6E1E4C7"
+	    "ABF5AE8C" "DB0933D7" "1E8C94E0" "4A25619D" "CEE3D226" "1AD2EE6B"
+	    "F12FFA06" "D98A0864" "D8760273" "3EC86A64" "521F2B18" "177B200C"
+	    "BBE11757" "7A615D6C" "770988C0" "BAD946E2" "08E24FA0" "74E5AB31"
+	    "43DB5BFC" "E0FD108E" "4B82D120" "A9210801" "1A723C12" "A787E6D7"
+	    "88719A10" "BDBA5B26" "99C32718" "6AF4E23C" "1A946834" "B6150BDA"
+	    "2583E9CA" "2AD44CE8" "DBBBC2DB" "04DE8EF9" "2E8EFC14" "1FBECAA6"
+	    "287C5947" "4E6BC05D" "99B2964F" "A090C3A2" "233BA186" "515BE7ED"
+	    "1F612970" "CEE2D7AF" "B81BDD76" "2170481C" "D0069127" "D5B05AA9"
+	    "93B4EA98" "8D8FDDC1" "86FFB7DC" "90A6C08F" "4DF435C9" "34063199"
+	    "FFFFFFFF" "FFFFFFFF";
+
+	if (max < 4096) {
+		debug3("requested max size %d, using 2k bit group 14", max);
+		return dh_new_group14();
+	}
+	debug3("using 4k bit group 16");
+	return (dh_new_group_asc(gen, group16));
+}
+
 /*
  * Estimates the group order for a Diffie-Hellman group that has an
  * attack complexity approximately the same as O(2**bits).
diff --git a/dh.h b/dh.h
index 63a1b1477..654695315 100644
--- a/dh.h
+++ b/dh.h
@@ -1,4 +1,4 @@
-/* $OpenBSD: dh.h,v 1.12 2015/01/19 20:16:15 markus Exp $ */
+/* $OpenBSD: dh.h,v 1.13 2015/05/27 23:39:18 dtucker Exp $ */
 
 /*
  * Copyright (c) 2000 Niels Provos.  All rights reserved.
@@ -37,6 +37,7 @@ DH	*dh_new_group_asc(const char *, const char *);
 DH	*dh_new_group(BIGNUM *, BIGNUM *);
 DH	*dh_new_group1(void);
 DH	*dh_new_group14(void);
+DH	*dh_new_group_fallback(int);
 
 int	 dh_gen_key(DH *, int);
 int	 dh_pub_is_valid(DH *, BIGNUM *);