diff --git a/ssl/s3_lib.c b/ssl/s3_lib.c
index 46e76e33c8b0aa2c47885b947047d66b3a6a6d42..a8f5637be5a6545376d417e02f8da9e436f68c8a 100644
--- a/ssl/s3_lib.c
+++ b/ssl/s3_lib.c
@@ -4621,6 +4621,43 @@ EVP_PKEY *ssl_generate_pkey_group(uint16_t id)
     EVP_PKEY_CTX_free(pctx);
     return pkey;
 }
+
+/*
+ * Generate parameters from a group ID
+ */
+EVP_PKEY *ssl_generate_param_group(uint16_t id)
+{
+    EVP_PKEY_CTX *pctx = NULL;
+    EVP_PKEY *pkey = NULL;
+    const TLS_GROUP_INFO *ginf = tls1_group_id_lookup(id);
+
+    if (ginf == NULL)
+        goto err;
+
+    if ((ginf->flags & TLS_CURVE_TYPE) == TLS_CURVE_CUSTOM) {
+        pkey = EVP_PKEY_new();
+        if (pkey != NULL && EVP_PKEY_set_type(pkey, ginf->nid))
+            return pkey;
+        EVP_PKEY_free(pkey);
+        return NULL;
+    }
+
+    pctx = EVP_PKEY_CTX_new_id(EVP_PKEY_EC, NULL);
+    if (pctx == NULL)
+        goto err;
+    if (EVP_PKEY_paramgen_init(pctx) <= 0)
+        goto err;
+    if (EVP_PKEY_CTX_set_ec_paramgen_curve_nid(pctx, ginf->nid) <= 0)
+        goto err;
+    if (EVP_PKEY_paramgen(pctx, &pkey) <= 0) {
+        EVP_PKEY_free(pkey);
+        pkey = NULL;
+    }
+
+ err:
+    EVP_PKEY_CTX_free(pctx);
+    return pkey;
+}
 #endif
 
 /* Derive secrets for ECDH/DH */
diff --git a/ssl/ssl_locl.h b/ssl/ssl_locl.h
index 029372e41e325caf14674162305a3c578de667e0..dc4a0f4701c94c5cba27d1f23f639cc578ef1009 100644
--- a/ssl/ssl_locl.h
+++ b/ssl/ssl_locl.h
@@ -2351,6 +2351,7 @@ void tls1_get_formatlist(SSL *s, const unsigned char **pformats,
                          size_t *num_formats);
 __owur int tls1_check_ec_tmp_key(SSL *s, unsigned long id);
 __owur EVP_PKEY *ssl_generate_pkey_group(uint16_t id);
+__owur EVP_PKEY *ssl_generate_param_group(uint16_t id);
 #  endif                        /* OPENSSL_NO_EC */
 
 __owur int tls_curve_allowed(SSL *s, uint16_t curve, int op);
diff --git a/ssl/statem/extensions_srvr.c b/ssl/statem/extensions_srvr.c
index 5fb0d05a2a1781c7da28d2bc159e838e3949d183..ebae44899a1952ce559fef56d09cfcfde70a60fa 100644
--- a/ssl/statem/extensions_srvr.c
+++ b/ssl/statem/extensions_srvr.c
@@ -502,7 +502,6 @@ int tls_parse_ctos_key_share(SSL *s, PACKET *pkt, unsigned int context, X509 *x,
     const uint16_t *clntcurves, *srvrcurves;
     size_t clnt_num_curves, srvr_num_curves;
     int found = 0;
-    const TLS_GROUP_INFO *ginf;
 
     if (s->hit && (s->ext.psk_kex_mode & TLSEXT_KEX_MODE_FLAG_KE_DHE) == 0)
         return 1;
@@ -575,43 +574,13 @@ int tls_parse_ctos_key_share(SSL *s, PACKET *pkt, unsigned int context, X509 *x,
             continue;
         }
 
-        ginf = tls1_group_id_lookup(group_id);
-
-        if (ginf == NULL) {
+        if ((s->s3->peer_tmp = ssl_generate_param_group(group_id)) == NULL) {
             *al = SSL_AD_INTERNAL_ERROR;
             SSLerr(SSL_F_TLS_PARSE_CTOS_KEY_SHARE,
                    SSL_R_UNABLE_TO_FIND_ECDH_PARAMETERS);
             return 0;
         }
 
-        if ((ginf->flags & TLS_CURVE_TYPE) == TLS_CURVE_CUSTOM) {
-            /* Can happen for some curves, e.g. X25519 */
-            EVP_PKEY *key = EVP_PKEY_new();
-
-            if (key == NULL || !EVP_PKEY_set_type(key, ginf->nid)) {
-                *al = SSL_AD_INTERNAL_ERROR;
-                SSLerr(SSL_F_TLS_PARSE_CTOS_KEY_SHARE, ERR_R_EVP_LIB);
-                EVP_PKEY_free(key);
-                return 0;
-            }
-            s->s3->peer_tmp = key;
-        } else {
-            /* Set up EVP_PKEY with named curve as parameters */
-            EVP_PKEY_CTX *pctx = EVP_PKEY_CTX_new_id(EVP_PKEY_EC, NULL);
-
-            if (pctx == NULL
-                    || EVP_PKEY_paramgen_init(pctx) <= 0
-                    || EVP_PKEY_CTX_set_ec_paramgen_curve_nid(pctx,
-                                                              ginf->nid) <= 0
-                    || EVP_PKEY_paramgen(pctx, &s->s3->peer_tmp) <= 0) {
-                *al = SSL_AD_INTERNAL_ERROR;
-                SSLerr(SSL_F_TLS_PARSE_CTOS_KEY_SHARE, ERR_R_EVP_LIB);
-                EVP_PKEY_CTX_free(pctx);
-                return 0;
-            }
-            EVP_PKEY_CTX_free(pctx);
-            pctx = NULL;
-        }
         s->s3->group_id = group_id;
 
         if (!EVP_PKEY_set1_tls_encodedpoint(s->s3->peer_tmp,
diff --git a/ssl/statem/statem_clnt.c b/ssl/statem/statem_clnt.c
index a20bf005932f0cf38ad22048bd9502a474159a8f..833450babd17607e24b96c3d0545f5d256b165fc 100644
--- a/ssl/statem/statem_clnt.c
+++ b/ssl/statem/statem_clnt.c
@@ -2041,8 +2041,6 @@ static int tls_process_ske_ecdhe(SSL *s, PACKET *pkt, EVP_PKEY **pkey, int *al)
 #ifndef OPENSSL_NO_EC
     PACKET encoded_pt;
     const unsigned char *ecparams;
-    const TLS_GROUP_INFO *ginf;
-    EVP_PKEY_CTX *pctx = NULL;
 
     /*
      * Extract elliptic curve parameters and the server's ephemeral ECDH
@@ -2064,41 +2062,13 @@ static int tls_process_ske_ecdhe(SSL *s, PACKET *pkt, EVP_PKEY **pkey, int *al)
         return 0;
     }
 
-    ginf = tls1_group_id_lookup(ecparams[2]);
-
-    if (ginf == NULL) {
+    if ((s->s3->peer_tmp = ssl_generate_param_group(ecparams[2])) == NULL) {
         *al = SSL_AD_INTERNAL_ERROR;
         SSLerr(SSL_F_TLS_PROCESS_SKE_ECDHE,
                SSL_R_UNABLE_TO_FIND_ECDH_PARAMETERS);
         return 0;
     }
 
-    if ((ginf->flags & TLS_CURVE_TYPE) == TLS_CURVE_CUSTOM) {
-        EVP_PKEY *key = EVP_PKEY_new();
-
-        if (key == NULL || !EVP_PKEY_set_type(key, ginf->nid)) {
-            *al = SSL_AD_INTERNAL_ERROR;
-            SSLerr(SSL_F_TLS_PROCESS_SKE_ECDHE, ERR_R_EVP_LIB);
-            EVP_PKEY_free(key);
-            return 0;
-        }
-        s->s3->peer_tmp = key;
-    } else {
-        /* Set up EVP_PKEY with named curve as parameters */
-        pctx = EVP_PKEY_CTX_new_id(EVP_PKEY_EC, NULL);
-        if (pctx == NULL
-            || EVP_PKEY_paramgen_init(pctx) <= 0
-            || EVP_PKEY_CTX_set_ec_paramgen_curve_nid(pctx, ginf->nid) <= 0
-            || EVP_PKEY_paramgen(pctx, &s->s3->peer_tmp) <= 0) {
-            *al = SSL_AD_INTERNAL_ERROR;
-            SSLerr(SSL_F_TLS_PROCESS_SKE_ECDHE, ERR_R_EVP_LIB);
-            EVP_PKEY_CTX_free(pctx);
-            return 0;
-        }
-        EVP_PKEY_CTX_free(pctx);
-        pctx = NULL;
-    }
-
     if (!PACKET_get_length_prefixed_1(pkt, &encoded_pt)) {
         *al = SSL_AD_DECODE_ERROR;
         SSLerr(SSL_F_TLS_PROCESS_SKE_ECDHE, SSL_R_LENGTH_MISMATCH);