diff --git a/ssl/ssl_err.c b/ssl/ssl_err.c
index a6d3412..705252c 100644
--- a/ssl/ssl_err.c
+++ b/ssl/ssl_err.c
@@ -329,6 +329,8 @@
     {ERR_FUNC(SSL_F_TLS_CONSTRUCT_FINISHED), "tls_construct_finished"},
     {ERR_FUNC(SSL_F_TLS_CONSTRUCT_HELLO_REQUEST),
      "tls_construct_hello_request"},
+    {ERR_FUNC(SSL_F_TLS_CONSTRUCT_HELLO_RETRY_REQUEST),
+     "tls_construct_hello_retry_request"},
     {ERR_FUNC(SSL_F_TLS_CONSTRUCT_NEW_SESSION_TICKET),
      "tls_construct_new_session_ticket"},
     {ERR_FUNC(SSL_F_TLS_CONSTRUCT_NEXT_PROTO), "tls_construct_next_proto"},
@@ -603,6 +605,7 @@
     {ERR_REASON(SSL_R_NO_RENEGOTIATION), "no renegotiation"},
     {ERR_REASON(SSL_R_NO_REQUIRED_DIGEST), "no required digest"},
     {ERR_REASON(SSL_R_NO_SHARED_CIPHER), "no shared cipher"},
+    {ERR_REASON(SSL_R_NO_SHARED_GROUPS), "no shared groups"},
     {ERR_REASON(SSL_R_NO_SHARED_SIGNATURE_ALGORITHMS),
      "no shared signature algorithms"},
     {ERR_REASON(SSL_R_NO_SRTP_PROFILES), "no srtp profiles"},
diff --git a/ssl/ssl_locl.h b/ssl/ssl_locl.h
index 2a23007..099f8cc 100644
--- a/ssl/ssl_locl.h
+++ b/ssl/ssl_locl.h
@@ -1005,6 +1005,9 @@
     unsigned char cert_verify_hash[EVP_MAX_MD_SIZE];
     size_t cert_verify_hash_len;
 
+    /* Flag to indicate whether we should send a HelloRetryRequest or not */
+    int hello_retry_request;
+
     /*
      * the session_id_context is used to ensure sessions are only reused in
      * the appropriate context
diff --git a/ssl/statem/extensions.c b/ssl/statem/extensions.c
index 4137f03..fd050f0 100644
--- a/ssl/statem/extensions.c
+++ b/ssl/statem/extensions.c
@@ -979,12 +979,18 @@
             && (!s->hit
                 || (s->ext.psk_kex_mode & TLSEXT_KEX_MODE_FLAG_KE) == 0)) {
         /* No suitable share */
-        /* TODO(TLS1.3): Send a HelloRetryRequest */
+        if (s->server && s->hello_retry_request == 0 && sent) {
+            s->hello_retry_request = 1;
+            return 1;
+        }
+
+        /* Nothing left we can do - just fail */
         *al = SSL_AD_HANDSHAKE_FAILURE;
         SSLerr(SSL_F_FINAL_KEY_SHARE, SSL_R_NO_SUITABLE_KEY_SHARE);
         return 0;
     }
 
+    s->hello_retry_request = 0;
     /*
      * For a client side resumption with no key_share we need to generate
      * the handshake secret (otherwise this is done during key_share
diff --git a/ssl/statem/extensions_clnt.c b/ssl/statem/extensions_clnt.c
index efae916..0038745 100644
--- a/ssl/statem/extensions_clnt.c
+++ b/ssl/statem/extensions_clnt.c
@@ -164,7 +164,7 @@
     }
     /* Copy curve ID if supported */
     for (i = 0; i < num_curves; i++, pcurvestmp += 2) {
-        if (tls_curve_allowed(s, pcurves, SSL_SECOP_CURVE_SUPPORTED)) {
+        if (tls_curve_allowed(s, pcurvestmp, SSL_SECOP_CURVE_SUPPORTED)) {
             if (!WPACKET_put_bytes_u8(pkt, pcurvestmp[0])
                 || !WPACKET_put_bytes_u8(pkt, pcurvestmp[1])) {
                     SSLerr(SSL_F_TLS_CONSTRUCT_CTOS_SUPPORTED_GROUPS,
diff --git a/ssl/statem/extensions_srvr.c b/ssl/statem/extensions_srvr.c
index c4d20e5..f7b7990 100644
--- a/ssl/statem/extensions_srvr.c
+++ b/ssl/statem/extensions_srvr.c
@@ -116,6 +116,8 @@
             return 0;
         }
 
+        OPENSSL_free(s->session->ext.hostname);
+        s->session->ext.hostname = NULL;
         if (!PACKET_strndup(&hostname, &s->session->ext.hostname)) {
             *al = TLS1_AD_INTERNAL_ERROR;
             return 0;
@@ -361,6 +363,9 @@
         }
     } while (PACKET_remaining(&protocol_list) != 0);
 
+    OPENSSL_free(s->s3->alpn_proposed);
+    s->s3->alpn_proposed = NULL;
+    s->s3->alpn_proposed_len = 0;
     if (!PACKET_memdup(&save_protocol_list,
                        &s->s3->alpn_proposed, &s->s3->alpn_proposed_len)) {
         *al = TLS1_AD_INTERNAL_ERROR;
@@ -659,6 +664,9 @@
         return 0;
     }
 
+    OPENSSL_free(s->session->ext.supportedgroups);
+    s->session->ext.supportedgroups = NULL;
+    s->session->ext.supportedgroups_len = 0;
     if (!PACKET_memdup(&supported_groups_list,
                        &s->session->ext.supportedgroups,
                        &s->session->ext.supportedgroups_len)) {
@@ -1024,7 +1032,65 @@
     EVP_PKEY *ckey = s->s3->peer_tmp, *skey = NULL;
 
     if (ckey == NULL) {
-        /* No key_share received from client; must be resuming. */
+        /* No key_share received from client */
+        if (s->hello_retry_request) {
+            const unsigned char *pcurves, *pcurvestmp, *clntcurves;
+            size_t num_curves, clnt_num_curves, i;
+
+            /* Get the clients list of supported groups. */
+            if (!tls1_get_curvelist(s, 1, &clntcurves, &clnt_num_curves)) {
+                *al = SSL_AD_INTERNAL_ERROR;
+                SSLerr(SSL_F_TLS_CONSTRUCT_STOC_KEY_SHARE,
+                       ERR_R_INTERNAL_ERROR);
+                return 0;
+            }
+
+            /* Get our list of available groups */
+            if (!tls1_get_curvelist(s, 0, &pcurves, &num_curves)) {
+                SSLerr(SSL_F_TLS_CONSTRUCT_STOC_KEY_SHARE,
+                       ERR_R_INTERNAL_ERROR);
+                return 0;
+            }
+
+            if (!WPACKET_put_bytes_u16(pkt, TLSEXT_TYPE_key_share)
+                    || !WPACKET_start_sub_packet_u16(pkt)) {
+                SSLerr(SSL_F_TLS_CONSTRUCT_STOC_KEY_SHARE,
+                       ERR_R_INTERNAL_ERROR);
+                return 0;
+            }
+
+            /* Find first group we allow that is also in client's list */
+            for (i = 0, pcurvestmp = pcurves; i < num_curves;
+                 i++, pcurvestmp += 2) {
+                unsigned int group_id = pcurvestmp[0] << 8 | pcurvestmp[1];
+
+                if (check_in_list(s, group_id, clntcurves, clnt_num_curves,
+                                  1)) {
+                    if (!WPACKET_put_bytes_u16(pkt, group_id)) {
+                        SSLerr(SSL_F_TLS_CONSTRUCT_STOC_KEY_SHARE,
+                               ERR_R_INTERNAL_ERROR);
+                        return 0;
+                    }
+                    break;
+                }
+            }
+            if (i == num_curves) {
+                /* No common groups */
+                *al = SSL_AD_HANDSHAKE_FAILURE;
+                SSLerr(SSL_F_TLS_CONSTRUCT_STOC_KEY_SHARE,
+                       SSL_R_NO_SHARED_GROUPS);
+                return 0;
+            }
+            if (!WPACKET_close(pkt)) {
+                SSLerr(SSL_F_TLS_CONSTRUCT_STOC_KEY_SHARE,
+                       ERR_R_INTERNAL_ERROR);
+                return 0;
+            }
+
+            return 1;
+        }
+
+        /* Must be resuming. */
         if (!s->hit || !tls13_generate_handshake_secret(s, NULL, 0)) {
             *al = SSL_AD_INTERNAL_ERROR;
             SSLerr(SSL_F_TLS_CONSTRUCT_STOC_KEY_SHARE, ERR_R_INTERNAL_ERROR);
diff --git a/ssl/statem/statem_lib.c b/ssl/statem/statem_lib.c
index 8e7245b..13174ab 100644
--- a/ssl/statem/statem_lib.c
+++ b/ssl/statem/statem_lib.c
@@ -1434,21 +1434,22 @@
 
     switch (server_version) {
     default:
+        if (!SSL_IS_TLS13(s)) {
+            if (version_cmp(s, client_version, s->version) < 0)
+                return SSL_R_WRONG_SSL_VERSION;
+            /*
+             * If this SSL handle is not from a version flexible method we don't
+             * (and never did) check min/max FIPS or Suite B constraints.  Hope
+             * that's OK.  It is up to the caller to not choose fixed protocol
+             * versions they don't want.  If not, then easy to fix, just return
+             * ssl_method_error(s, s->method)
+             */
+            return 0;
+        }
         /*
-         * TODO(TLS1.3): This check will fail if someone attempts to do
-         * renegotiation in TLS1.3 at the moment. We need to ensure we disable
-         * renegotiation for TLS1.3
+         * Fall through if we are TLSv1.3 already (this means we must be after
+         * a HelloRetryRequest
          */
-        if (version_cmp(s, client_version, s->version) < 0)
-            return SSL_R_WRONG_SSL_VERSION;
-        /*
-         * If this SSL handle is not from a version flexible method we don't
-         * (and never did) check min/max FIPS or Suite B constraints.  Hope
-         * that's OK.  It is up to the caller to not choose fixed protocol
-         * versions they don't want.  If not, then easy to fix, just return
-         * ssl_method_error(s, s->method)
-         */
-        return 0;
     case TLS_ANY_VERSION:
         table = tls_version_table;
         break;
@@ -1503,6 +1504,15 @@
         }
 
         if (best_vers > 0) {
+            if (SSL_IS_TLS13(s)) {
+                /*
+                 * We get here if this is after a HelloRetryRequest. In this
+                 * case we just check that we still negotiated TLSv1.3
+                 */
+                if (best_vers != TLS1_3_VERSION)
+                    return SSL_R_UNSUPPORTED_PROTOCOL;
+                return 0;
+            }
             s->version = best_vers;
             s->method = best_method;
             return 0;
diff --git a/ssl/statem/statem_srvr.c b/ssl/statem/statem_srvr.c
index de0fcc0..8aba669 100644
--- a/ssl/statem/statem_srvr.c
+++ b/ssl/statem/statem_srvr.c
@@ -62,6 +62,7 @@
 #include <openssl/md5.h>
 
 static int tls_construct_encrypted_extensions(SSL *s, WPACKET *pkt);
+static int tls_construct_hello_retry_request(SSL *s, WPACKET *pkt);
 static STACK_OF(SSL_CIPHER) *ssl_bytes_to_cipher_list(SSL *s,
                                                       PACKET *cipher_suites,
                                                       STACK_OF(SSL_CIPHER)
@@ -82,11 +83,6 @@
     OSSL_STATEM *st = &s->statem;
 
     /*
-     * TODO(TLS1.3): This is still based on the TLSv1.2 state machine. Over time
-     * we will update this to look more like real TLSv1.3
-     */
-
-    /*
      * Note: There is no case for TLS_ST_BEFORE because at that stage we have
      * not negotiated TLSv1.3 yet, so that case is handled by
      * ossl_statem_server_read_transition()
@@ -95,6 +91,13 @@
     default:
         break;
 
+    case TLS_ST_SW_HELLO_RETRY_REQUEST:
+        if (mt == SSL3_MT_CLIENT_HELLO) {
+            st->hand_state = TLS_ST_SR_CLNT_HELLO;
+            return 1;
+        }
+        break;
+
     case TLS_ST_SW_FINISHED:
         if (s->s3->tmp.cert_request) {
             if (mt == SSL3_MT_CERTIFICATE) {
@@ -406,9 +409,15 @@
         return WRITE_TRAN_ERROR;
 
     case TLS_ST_SR_CLNT_HELLO:
-        st->hand_state = TLS_ST_SW_SRVR_HELLO;
+        if (s->hello_retry_request)
+            st->hand_state = TLS_ST_SW_HELLO_RETRY_REQUEST;
+        else
+            st->hand_state = TLS_ST_SW_SRVR_HELLO;
         return WRITE_TRAN_CONTINUE;
 
+    case TLS_ST_SW_HELLO_RETRY_REQUEST:
+        return WRITE_TRAN_FINISHED;
+
     case TLS_ST_SW_SRVR_HELLO:
         st->hand_state = TLS_ST_SW_ENCRYPTED_EXTENSIONS;
         return WRITE_TRAN_CONTINUE;
@@ -693,6 +702,11 @@
         /* No post work to be done */
         break;
 
+    case TLS_ST_SW_HELLO_RETRY_REQUEST:
+        if (statem_flush(s) != 1)
+            return WORK_MORE_A;
+        break;
+
     case TLS_ST_SW_HELLO_REQ:
         if (statem_flush(s) != 1)
             return WORK_MORE_A;
@@ -904,6 +918,11 @@
         *confunc = tls_construct_encrypted_extensions;
         *mt = SSL3_MT_ENCRYPTED_EXTENSIONS;
         break;
+
+    case TLS_ST_SW_HELLO_RETRY_REQUEST:
+        *confunc = tls_construct_hello_retry_request;
+        *mt = SSL3_MT_HELLO_RETRY_REQUEST;
+        break;
     }
 
     return 1;
@@ -1200,6 +1219,12 @@
     if (clienthello.isv2) {
         unsigned int mt;
 
+        if (!SSL_IS_FIRST_HANDSHAKE(s) || s->hello_retry_request) {
+            al = SSL_AD_HANDSHAKE_FAILURE;
+            SSLerr(SSL_F_TLS_PROCESS_CLIENT_HELLO, SSL_R_UNEXPECTED_MESSAGE);
+            goto f_err;
+        }
+
         /*-
          * An SSLv3/TLSv1 backwards-compatible CLIENT-HELLO in an SSLv2
          * header is sent directly on the wire, not wrapped as a TLS
@@ -1402,7 +1427,7 @@
 
     if (protverr) {
         SSLerr(SSL_F_TLS_PROCESS_CLIENT_HELLO, protverr);
-        if ((!s->enc_write_ctx && !s->write_hash)) {
+        if (SSL_IS_FIRST_HANDSHAKE(s)) {
             /* like ssl3_get_record, send alert using remote version number */
             s->version = s->client_version = clienthello.legacy_version;
         }
@@ -3502,6 +3527,10 @@
         return NULL;
     }
 
+    OPENSSL_free(s->s3->tmp.ciphers_raw);
+    s->s3->tmp.ciphers_raw = NULL;
+    s->s3->tmp.ciphers_rawlen = 0;
+
     if (sslv2format) {
         size_t numciphers = PACKET_remaining(cipher_suites) / n;
         PACKET sslv2ciphers = *cipher_suites;
@@ -3607,3 +3636,28 @@
     sk_SSL_CIPHER_free(sk);
     return NULL;
 }
+
+static int tls_construct_hello_retry_request(SSL *s, WPACKET *pkt)
+{
+    int al;
+
+    /*
+     * TODO(TLS1.3): Remove the DRAFT version before release
+     * (should be s->version)
+     */
+    if (!WPACKET_put_bytes_u16(pkt, TLS1_3_VERSION_DRAFT)
+            || !tls_construct_extensions(s, pkt, EXT_TLS1_3_HELLO_RETRY_REQUEST,
+                                         NULL, 0, &al)) {
+        ssl3_send_alert(s, SSL3_AL_FATAL, al);
+        SSLerr(SSL_F_TLS_CONSTRUCT_HELLO_RETRY_REQUEST, ERR_R_INTERNAL_ERROR);
+        ssl3_send_alert(s, SSL3_AL_FATAL, al);
+        return 0;
+    }
+
+    /* Ditch the session. We'll create a new one next time around */
+    SSL_SESSION_free(s->session);
+    s->session = NULL;
+    s->hit = 0;
+
+    return 1;
+}