diff --git a/ssl/t1_lib.c b/ssl/t1_lib.c
index dbd0fb6cc6..6f7ef965be 100644
--- a/ssl/t1_lib.c
+++ b/ssl/t1_lib.c
@@ -1278,6 +1278,7 @@ int tls12_get_sigandhash(SSL *s, WPACKET *pkt, const EVP_PKEY *pk,
 {
     int md_id, sig_id;
     size_t i;
+    const SIGALG_LOOKUP *curr;
 
     if (md == NULL)
         return 0;
@@ -1289,8 +1290,25 @@ int tls12_get_sigandhash(SSL *s, WPACKET *pkt, const EVP_PKEY *pk,
     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++) {
-        const SIGALG_LOOKUP *curr = s->cert->shared_sigalgs[i];
+        curr = s->cert->shared_sigalgs[i];
 
         /*
          * Look for matching key and hash. If key type is RSA also match PSS