diff --git a/ssl/ssl_locl.h b/ssl/ssl_locl.h
index e1bce30a20..6f838778a6 100644
--- a/ssl/ssl_locl.h
+++ b/ssl/ssl_locl.h
@@ -2260,8 +2260,6 @@ __owur TICKET_RETURN tls_decrypt_ticket(SSL *s, const unsigned char *etick,
 
 __owur int tls_use_ticket(SSL *s);
 
-__owur int tls12_get_sigandhash(SSL *s, WPACKET *pkt, const EVP_PKEY *pk,
-                                const EVP_MD *md, int *ispss);
 void ssl_set_sig_mask(uint32_t *pmask_a, SSL *s, int op);
 
 __owur int tls1_set_sigalgs_list(CERT *c, const char *str, int client);
diff --git a/ssl/statem/statem_clnt.c b/ssl/statem/statem_clnt.c
index 8ca3c4cc1d..4923e245ff 100644
--- a/ssl/statem/statem_clnt.c
+++ b/ssl/statem/statem_clnt.c
@@ -3090,10 +3090,8 @@ int tls_client_key_exchange_post_work(SSL *s)
  */
 static int ssl3_check_client_certificate(SSL *s)
 {
-    if (!s->cert || !s->cert->key->x509 || !s->cert->key->privatekey)
-        return 0;
     /* If no suitable signature algorithm can't use certificate */
-    if (SSL_USE_SIGALGS(s) && !s->s3->tmp.md[s->cert->key - s->cert->pkeys])
+    if (!tls_choose_sigalg(s, NULL) || s->s3->tmp.sigalg == NULL)
         return 0;
     /*
      * If strict mode check suitability of chain before using it. This also
diff --git a/ssl/statem/statem_lib.c b/ssl/statem/statem_lib.c
index 31156fdcc8..ed07266c01 100644
--- a/ssl/statem/statem_lib.c
+++ b/ssl/statem/statem_lib.c
@@ -171,17 +171,27 @@ static int get_cert_verify_tbs_data(SSL *s, unsigned char *tls13tbs,
 
 int tls_construct_cert_verify(SSL *s, WPACKET *pkt)
 {
-    EVP_PKEY *pkey = s->cert->key->privatekey;
-    const EVP_MD *md = s->s3->tmp.md[s->cert->key - s->cert->pkeys];
+    EVP_PKEY *pkey = NULL;
+    const EVP_MD *md = NULL;
     EVP_MD_CTX *mctx = NULL;
     EVP_PKEY_CTX *pctx = NULL;
     size_t hdatalen = 0, siglen = 0;
     void *hdata;
     unsigned char *sig = NULL;
     unsigned char tls13tbs[TLS13_TBS_PREAMBLE_SIZE + EVP_MAX_MD_SIZE];
-    int pktype, ispss = 0;
+    const SIGALG_LOOKUP *lu = s->s3->tmp.sigalg;
 
-    pktype = EVP_PKEY_id(pkey);
+    if (lu == NULL || s->s3->tmp.cert == NULL) {
+        SSLerr(SSL_F_TLS_CONSTRUCT_CERT_VERIFY, ERR_R_INTERNAL_ERROR);
+        goto err;
+    }
+    pkey = s->s3->tmp.cert->privatekey;
+    md = ssl_md(lu->hash_idx);
+
+    if (pkey == NULL || md == NULL) {
+        SSLerr(SSL_F_TLS_CONSTRUCT_CERT_VERIFY, ERR_R_INTERNAL_ERROR);
+        goto err;
+    }
 
     mctx = EVP_MD_CTX_new();
     if (mctx == NULL) {
@@ -195,13 +205,10 @@ int tls_construct_cert_verify(SSL *s, WPACKET *pkt)
         goto err;
     }
 
-    if (SSL_USE_SIGALGS(s) && !tls12_get_sigandhash(s, pkt, pkey, md, &ispss)) {
+    if (SSL_USE_SIGALGS(s) && !WPACKET_put_bytes_u16(pkt, lu->sigalg)) {
         SSLerr(SSL_F_TLS_CONSTRUCT_CERT_VERIFY, ERR_R_INTERNAL_ERROR);
         goto err;
     }
-#ifdef SSL_DEBUG
-    fprintf(stderr, "Using client alg %s\n", EVP_MD_name(md));
-#endif
     siglen = EVP_PKEY_size(pkey);
     sig = OPENSSL_malloc(siglen);
     if (sig == NULL) {
@@ -215,7 +222,7 @@ int tls_construct_cert_verify(SSL *s, WPACKET *pkt)
         goto err;
     }
 
-    if (ispss) {
+    if (lu->sig == EVP_PKEY_RSA_PSS) {
         if (EVP_PKEY_CTX_set_rsa_padding(pctx, RSA_PKCS1_PSS_PADDING) <= 0
             || EVP_PKEY_CTX_set_rsa_pss_saltlen(pctx,
                                                 RSA_PSS_SALTLEN_DIGEST) <= 0) {
@@ -238,6 +245,8 @@ int tls_construct_cert_verify(SSL *s, WPACKET *pkt)
 
 #ifndef OPENSSL_NO_GOST
     {
+        int pktype = lu->sig;
+
         if (pktype == NID_id_GostR3410_2001
             || pktype == NID_id_GostR3410_2012_256
             || pktype == NID_id_GostR3410_2012_512)
diff --git a/ssl/t1_lib.c b/ssl/t1_lib.c
index 5f44f5a112..fc9ae687f6 100644
--- a/ssl/t1_lib.c
+++ b/ssl/t1_lib.c
@@ -1349,58 +1349,6 @@ TICKET_RETURN tls_decrypt_ticket(SSL *s, const unsigned char *etick,
     return ret;
 }
 
-int tls12_get_sigandhash(SSL *s, WPACKET *pkt, const EVP_PKEY *pk,
-                         const EVP_MD *md, int *ispss)
-{
-    int md_id, sig_id;
-    size_t i;
-    const SIGALG_LOOKUP *curr;
-
-    if (md == NULL)
-        return 0;
-    md_id = EVP_MD_type(md);
-    sig_id = EVP_PKEY_id(pk);
-    if (md_id == NID_undef)
-        return 0;
-    /* For TLS 1.3 only allow RSA-PSS */
-    if (SSL_IS_TLS13(s) && sig_id == EVP_PKEY_RSA)
-        sig_id = EVP_PKEY_RSA_PSS;
-
-    if (s->s3->tmp.peer_sigalgs == NULL) {
-        /* Should never happen: we abort if no sigalgs extension and TLS 1.3 */
-        if (SSL_IS_TLS13(s))
-            return 0;
-        /* For TLS 1.2 and no sigalgs lookup using complete table */
-        for (i = 0, curr = sigalg_lookup_tbl; i < OSSL_NELEM(sigalg_lookup_tbl);
-             i++, curr++) {
-            if (curr->hash == md_id && curr->sig == sig_id) {
-                if (!WPACKET_put_bytes_u16(pkt, curr->sigalg))
-                    return 0;
-                *ispss = curr->sig == EVP_PKEY_RSA_PSS;
-                return 1;
-            }
-        }
-        return 0;
-    }
-
-    for (i = 0; i < s->cert->shared_sigalgslen; i++) {
-        curr = s->cert->shared_sigalgs[i];
-
-        /*
-         * Look for matching key and hash. If key type is RSA also match PSS
-         * signature type.
-         */
-        if (curr->hash == md_id && (curr->sig == sig_id
-            || (sig_id == EVP_PKEY_RSA && curr->sig == EVP_PKEY_RSA_PSS))){
-            if (!WPACKET_put_bytes_u16(pkt, curr->sigalg))
-                return 0;
-            *ispss = curr->sig == EVP_PKEY_RSA_PSS;
-            return 1;
-        }
-    }
-    return 0;
-}
-
 static int tls12_get_pkey_idx(int sig_nid)
 {
     switch (sig_nid) {