diff --git a/include/openssl/ssl.h b/include/openssl/ssl.h
index a62108b..b61df9d 100644
--- a/include/openssl/ssl.h
+++ b/include/openssl/ssl.h
@@ -1791,20 +1791,6 @@
 OPENSSL_EXPORT int SSL_set1_curves(SSL *ssl, const int *curves,
                                    size_t curves_len);
 
-/* SSL_CTX_set_tmp_ecdh configures |ctx| to use the curve from |ecdh| as the
- * curve for ephemeral ECDH keys. For historical reasons, this API expects an
- * |EC_KEY|, but only the curve is used. It returns one on success and zero on
- * error. If unset, an appropriate curve will be chosen based on curve
- * preferences. (This is recommended.) */
-OPENSSL_EXPORT int SSL_CTX_set_tmp_ecdh(SSL_CTX *ctx, const EC_KEY *ec_key);
-
-/* SSL_set_tmp_ecdh configures |ssl| to use the curve from |ecdh| as the curve
- * for ephemeral ECDH keys. For historical reasons, this API expects an
- * |EC_KEY|, but only the curve is used. It returns one on success and zero on
- * error. If unset, an appropriate curve will be chosen based on curve
- * preferences. (This is recommended.) */
-OPENSSL_EXPORT int SSL_set_tmp_ecdh(SSL *ssl, const EC_KEY *ec_key);
-
 /* SSL_get_curve_name returns a human-readable name for the elliptic curve
  * specified by the given TLS curve id, or NULL if the curve if unknown. */
 OPENSSL_EXPORT const char *SSL_get_curve_name(uint16_t curve_id);
@@ -3304,6 +3290,14 @@
  * Use |SSL_CTX_set_quiet_shutdown| instead. */
 OPENSSL_EXPORT void SSL_set_shutdown(SSL *ssl, int mode);
 
+/* SSL_CTX_set_tmp_ecdh calls |SSL_CTX_set1_curves| with a one-element list
+ * containing |ec_key|'s curve. */
+OPENSSL_EXPORT int SSL_CTX_set_tmp_ecdh(SSL_CTX *ctx, const EC_KEY *ec_key);
+
+/* SSL_set_tmp_ecdh calls |SSL_set1_curves| with a one-element list containing
+ * |ec_key|'s curve. */
+OPENSSL_EXPORT int SSL_set_tmp_ecdh(SSL *ssl, const EC_KEY *ec_key);
+
 
 /* Private structures.
  *
diff --git a/ssl/internal.h b/ssl/internal.h
index 73387a0..dde605b 100644
--- a/ssl/internal.h
+++ b/ssl/internal.h
@@ -726,10 +726,6 @@
   DH *dh_tmp;
   DH *(*dh_tmp_cb)(SSL *ssl, int is_export, int keysize);
 
-  /* ecdh_nid, if not |NID_undef|, is the NID of the curve to use for ephemeral
-   * ECDH keys. */
-  int ecdh_nid;
-
   /* peer_sigalgs are the algorithm/hash pairs that the peer supports. These
    * are taken from the contents of signature algorithms extension for a server
    * or from the CertificateRequest for a client. */
@@ -1172,10 +1168,6 @@
  * zero. */
 int tls1_check_ec_cert(SSL *s, X509 *x);
 
-/* tls1_check_ec_tmp_key returns one if the EC temporary key is compatible with
- * client extensions and zero otherwise. */
-int tls1_check_ec_tmp_key(SSL *s);
-
 int tls1_shared_list(SSL *s, const uint8_t *l1, size_t l1len, const uint8_t *l2,
                      size_t l2len, int nmatch);
 
diff --git a/ssl/s3_lib.c b/ssl/s3_lib.c
index f6d400a..3f8cea0 100644
--- a/ssl/s3_lib.c
+++ b/ssl/s3_lib.c
@@ -299,8 +299,8 @@
     OPENSSL_PUT_ERROR(SSL, ERR_R_PASSED_NULL_PARAMETER);
     return 0;
   }
-  ctx->cert->ecdh_nid = EC_GROUP_get_curve_name(EC_KEY_get0_group(ec_key));
-  return 1;
+  int nid = EC_GROUP_get_curve_name(EC_KEY_get0_group(ec_key));
+  return SSL_CTX_set1_curves(ctx, &nid, 1);
 }
 
 int SSL_set_tmp_ecdh(SSL *ssl, const EC_KEY *ec_key) {
@@ -308,8 +308,8 @@
     OPENSSL_PUT_ERROR(SSL, ERR_R_PASSED_NULL_PARAMETER);
     return 0;
   }
-  ssl->cert->ecdh_nid = EC_GROUP_get_curve_name(EC_KEY_get0_group(ec_key));
-  return 1;
+  int nid = EC_GROUP_get_curve_name(EC_KEY_get0_group(ec_key));
+  return SSL_set1_curves(ssl, &nid, 1);
 }
 
 int SSL_CTX_enable_tls_channel_id(SSL_CTX *ctx) {
diff --git a/ssl/s3_srvr.c b/ssl/s3_srvr.c
index 04cae2e..13e1d35 100644
--- a/ssl/s3_srvr.c
+++ b/ssl/s3_srvr.c
@@ -1299,12 +1299,7 @@
       r_pad_bytes[2] = BN_num_bytes(dh->p) - BN_num_bytes(dh->pub_key);
     } else if (alg_k & SSL_kECDHE) {
       /* Determine the curve to use. */
-      int nid = NID_undef;
-      if (cert->ecdh_nid != NID_undef) {
-        nid = cert->ecdh_nid;
-      } else {
-        nid = tls1_get_shared_curve(s);
-      }
+      int nid = tls1_get_shared_curve(s);
       if (nid == NID_undef) {
         al = SSL_AD_HANDSHAKE_FAILURE;
         OPENSSL_PUT_ERROR(SSL, SSL_R_MISSING_TMP_ECDH_KEY);
diff --git a/ssl/ssl_cert.c b/ssl/ssl_cert.c
index 8788152..bb83f88 100644
--- a/ssl/ssl_cert.c
+++ b/ssl/ssl_cert.c
@@ -185,8 +185,6 @@
   }
   ret->dh_tmp_cb = cert->dh_tmp_cb;
 
-  ret->ecdh_nid = cert->ecdh_nid;
-
   if (cert->x509 != NULL) {
     ret->x509 = X509_up_ref(cert->x509);
   }
diff --git a/ssl/ssl_lib.c b/ssl/ssl_lib.c
index 379fd4f..5e4d997 100644
--- a/ssl/ssl_lib.c
+++ b/ssl/ssl_lib.c
@@ -1785,8 +1785,8 @@
   }
 
   /* If we are considering an ECC cipher suite that uses an ephemeral EC
-   * key, check it. */
-  if (tls1_check_ec_tmp_key(s)) {
+   * key, check for a shared curve. */
+  if (tls1_get_shared_curve(s) != NID_undef) {
     mask_k |= SSL_kECDHE;
   }
 
diff --git a/ssl/t1_lib.c b/ssl/t1_lib.c
index 0e78594..f0b792e 100644
--- a/ssl/t1_lib.c
+++ b/ssl/t1_lib.c
@@ -602,20 +602,6 @@
   return ret;
 }
 
-int tls1_check_ec_tmp_key(SSL *s) {
-  if (s->cert->ecdh_nid != NID_undef) {
-    /* If the curve is preconfigured, ECDH is acceptable iff the peer supports
-     * the curve. */
-    uint16_t curve_id;
-    return tls1_ec_nid2curve_id(&curve_id, s->cert->ecdh_nid) &&
-           tls1_check_curve_id(s, curve_id);
-  }
-
-  /* Otherwise, the curve gets selected automatically. ECDH is acceptable iff
-   * there is a shared curve. */
-  return tls1_get_shared_curve(s) != NID_undef;
-}
-
 /* List of supported signature algorithms and hashes. Should make this
  * customisable at some point, for now include everything we support. */