diff --git a/apps/apps.h b/apps/apps.h
index 4ec0693b30..09c601b62f 100644
--- a/apps/apps.h
+++ b/apps/apps.h
@@ -214,10 +214,11 @@ int set_cert_times(X509 *x, const char *startdate, const char *enddate,
         OPT_S_NOSSL3, OPT_S_NOTLS1, OPT_S_NOTLS1_1, OPT_S_NOTLS1_2, \
         OPT_S_NOTLS1_3, OPT_S_BUGS, OPT_S_NO_COMP, OPT_S_NOTICKET, \
         OPT_S_SERVERPREF, OPT_S_LEGACYRENEG, OPT_S_LEGACYCONN, \
-        OPT_S_ONRESUMP, OPT_S_NOLEGACYCONN, OPT_S_STRICT, OPT_S_SIGALGS, \
-        OPT_S_CLIENTSIGALGS, OPT_S_GROUPS, OPT_S_CURVES, OPT_S_NAMEDCURVE, \
-        OPT_S_CIPHER, OPT_S_DHPARAM, OPT_S_RECORD_PADDING, OPT_S_DEBUGBROKE, \
-        OPT_S_COMP, OPT_S_NO_RENEGOTIATION, OPT_S__LAST
+        OPT_S_ONRESUMP, OPT_S_NOLEGACYCONN, OPT_S_ALLOW_NO_DHE_KEX, \
+        OPT_S_STRICT, OPT_S_SIGALGS, OPT_S_CLIENTSIGALGS, OPT_S_GROUPS, \
+        OPT_S_CURVES, OPT_S_NAMEDCURVE, OPT_S_CIPHER, OPT_S_DHPARAM, \
+        OPT_S_RECORD_PADDING, OPT_S_DEBUGBROKE, OPT_S_COMP, \
+        OPT_S_NO_RENEGOTIATION, OPT_S__LAST
 
 # define OPT_S_OPTIONS \
         {"no_ssl3", OPT_S_NOSSL3, '-',"Just disable SSLv3" }, \
@@ -241,6 +242,8 @@ int set_cert_times(X509 *x, const char *startdate, const char *enddate,
             "Disallow session resumption on renegotiation"}, \
         {"no_legacy_server_connect", OPT_S_NOLEGACYCONN, '-', \
             "Disallow initial connection to servers that don't support RI"}, \
+        {"allow_no_dhe_kex", OPT_S_ALLOW_NO_DHE_KEX, '-', \
+            "In TLSv1.3 allow non-(ec)dhe based key exchange on resumption"}, \
         {"strict", OPT_S_STRICT, '-', \
             "Enforce strict certificate checks as per TLS standard"}, \
         {"sigalgs", OPT_S_SIGALGS, 's', \
@@ -279,6 +282,7 @@ int set_cert_times(X509 *x, const char *startdate, const char *enddate,
         case OPT_S_LEGACYCONN: \
         case OPT_S_ONRESUMP: \
         case OPT_S_NOLEGACYCONN: \
+        case OPT_S_ALLOW_NO_DHE_KEX: \
         case OPT_S_STRICT: \
         case OPT_S_SIGALGS: \
         case OPT_S_CLIENTSIGALGS: \
diff --git a/include/openssl/ssl.h b/include/openssl/ssl.h
index 75fb1fcc7f..cc5b398a16 100644
--- a/include/openssl/ssl.h
+++ b/include/openssl/ssl.h
@@ -282,6 +282,9 @@ typedef int (*SSL_custom_ext_parse_cb_ex) (SSL *s, unsigned int ext_type,
 /* Typedef for verification callback */
 typedef int (*SSL_verify_cb)(int preverify_ok, X509_STORE_CTX *x509_ctx);
 
+/* In TLSv1.3 allow a non-(ec)dhe based kex_mode */
+# define SSL_OP_ALLOW_NO_DHE_KEX                         0x00000001U
+
 /* Allow initial connection to servers that don't support RI */
 # define SSL_OP_LEGACY_SERVER_CONNECT                    0x00000004U
 # define SSL_OP_TLSEXT_PADDING                           0x00000010U
diff --git a/ssl/ssl_conf.c b/ssl/ssl_conf.c
index ab0a94ddd7..6dd5922a54 100644
--- a/ssl/ssl_conf.c
+++ b/ssl/ssl_conf.c
@@ -367,6 +367,7 @@ static int cmd_Options(SSL_CONF_CTX *cctx, const char *value)
                      SSL_OP_ALLOW_UNSAFE_LEGACY_RENEGOTIATION),
         SSL_FLAG_TBL_INV("EncryptThenMac", SSL_OP_NO_ENCRYPT_THEN_MAC),
         SSL_FLAG_TBL("NoRenegotiation", SSL_OP_NO_RENEGOTIATION),
+        SSL_FLAG_TBL("AllowNoDHEKEX", SSL_OP_ALLOW_NO_DHE_KEX)
     };
     if (value == NULL)
         return -3;
@@ -585,6 +586,7 @@ static const ssl_conf_cmd_tbl ssl_conf_cmds[] = {
     SSL_CONF_CMD_SWITCH("no_renegotiation", 0),
     SSL_CONF_CMD_SWITCH("no_resumption_on_reneg", SSL_CONF_FLAG_SERVER),
     SSL_CONF_CMD_SWITCH("no_legacy_server_connect", SSL_CONF_FLAG_SERVER),
+    SSL_CONF_CMD_SWITCH("allow_no_dhe_kex", 0),
     SSL_CONF_CMD_SWITCH("strict", 0),
     SSL_CONF_CMD_STRING(SignatureAlgorithms, "sigalgs", 0),
     SSL_CONF_CMD_STRING(ClientSignatureAlgorithms, "client_sigalgs", 0),
@@ -655,6 +657,8 @@ static const ssl_switch_tbl ssl_cmd_switches[] = {
     {SSL_OP_NO_SESSION_RESUMPTION_ON_RENEGOTIATION, 0},
     /* no_legacy_server_connect */
     {SSL_OP_LEGACY_SERVER_CONNECT, SSL_TFLAG_INV},
+    /* allow_no_dhe_kex */
+    {SSL_OP_ALLOW_NO_DHE_KEX, 0},
     {SSL_CERT_FLAG_TLS_STRICT, SSL_TFLAG_CERT}, /* strict */
 };
 
diff --git a/ssl/statem/extensions_clnt.c b/ssl/statem/extensions_clnt.c
index 0d1ca281f7..1bbb2102d7 100644
--- a/ssl/statem/extensions_clnt.c
+++ b/ssl/statem/extensions_clnt.c
@@ -503,30 +503,29 @@ EXT_RETURN tls_construct_ctos_supported_versions(SSL *s, WPACKET *pkt,
 }
 
 /*
- * Construct a psk_kex_modes extension. We only have two modes we know about
- * at this stage, so we send both.
+ * Construct a psk_kex_modes extension.
  */
 EXT_RETURN tls_construct_ctos_psk_kex_modes(SSL *s, WPACKET *pkt,
                                             unsigned int context, X509 *x,
                                             size_t chainidx, int *al)
 {
 #ifndef OPENSSL_NO_TLS1_3
-    /*
-     * TODO(TLS1.3): Do we want this list to be configurable? For now we always
-     * just send both supported modes
-     */
+    int nodhe = s->options & SSL_OP_ALLOW_NO_DHE_KEX;
+
     if (!WPACKET_put_bytes_u16(pkt, TLSEXT_TYPE_psk_kex_modes)
             || !WPACKET_start_sub_packet_u16(pkt)
             || !WPACKET_start_sub_packet_u8(pkt)
             || !WPACKET_put_bytes_u8(pkt, TLSEXT_KEX_MODE_KE_DHE)
-            || !WPACKET_put_bytes_u8(pkt, TLSEXT_KEX_MODE_KE)
+            || (nodhe && !WPACKET_put_bytes_u8(pkt, TLSEXT_KEX_MODE_KE))
             || !WPACKET_close(pkt)
             || !WPACKET_close(pkt)) {
         SSLerr(SSL_F_TLS_CONSTRUCT_CTOS_PSK_KEX_MODES, ERR_R_INTERNAL_ERROR);
         return EXT_RETURN_FAIL;
     }
 
-    s->ext.psk_kex_mode = TLSEXT_KEX_MODE_FLAG_KE | TLSEXT_KEX_MODE_FLAG_KE_DHE;
+    s->ext.psk_kex_mode = TLSEXT_KEX_MODE_FLAG_KE_DHE;
+    if (nodhe)
+        s->ext.psk_kex_mode |= TLSEXT_KEX_MODE_FLAG_KE;
 #endif
 
     return EXT_RETURN_SENT;
diff --git a/ssl/statem/extensions_srvr.c b/ssl/statem/extensions_srvr.c
index 3da9f556e9..7f30ac7792 100644
--- a/ssl/statem/extensions_srvr.c
+++ b/ssl/statem/extensions_srvr.c
@@ -477,7 +477,8 @@ int tls_parse_ctos_psk_kex_modes(SSL *s, PACKET *pkt, unsigned int context,
     while (PACKET_get_1(&psk_kex_modes, &mode)) {
         if (mode == TLSEXT_KEX_MODE_KE_DHE)
             s->ext.psk_kex_mode |= TLSEXT_KEX_MODE_FLAG_KE_DHE;
-        else if (mode == TLSEXT_KEX_MODE_KE)
+        else if (mode == TLSEXT_KEX_MODE_KE
+                && (s->options & SSL_OP_ALLOW_NO_DHE_KEX) != 0)
             s->ext.psk_kex_mode |= TLSEXT_KEX_MODE_FLAG_KE;
     }
 #endif
diff --git a/test/recipes/70-test_tls13kexmodes.t b/test/recipes/70-test_tls13kexmodes.t
index 07020c686e..ec23e132e2 100644
--- a/test/recipes/70-test_tls13kexmodes.t
+++ b/test/recipes/70-test_tls13kexmodes.t
@@ -171,7 +171,8 @@ ok(TLSProxy::Message->fail(), "Resume with empty kex modes");
 #Test 4: Attempt a resume with non-dhe kex mode only. Should resume without a
 #        key_share
 $proxy->clear();
-$proxy->clientflags("-sess_in ".$session);
+$proxy->clientflags("-allow_no_dhe_kex -sess_in ".$session);
+$proxy->serverflags("-allow_no_dhe_kex");
 $testtype = NON_DHE_KEX_MODE_ONLY;
 $proxy->start();
 checkhandshake($proxy, checkhandshake::RESUME_HANDSHAKE,
@@ -256,8 +257,8 @@ checkhandshake($proxy, checkhandshake::HRR_RESUME_HANDSHAKE,
 #         initial key_share and no overlapping groups. Should resume without a
 #         key_share
 $proxy->clear();
-$proxy->clientflags("-curves P-384 -sess_in ".$session);
-$proxy->serverflags("-curves P-256");
+$proxy->clientflags("-allow_no_dhe_kex -curves P-384 -sess_in ".$session);
+$proxy->serverflags("-allow_no_dhe_kex -curves P-256");
 $testtype = BOTH_KEX_MODES;
 $proxy->start();
 checkhandshake($proxy, checkhandshake::RESUME_HANDSHAKE,