diff --git a/ssl/internal.h b/ssl/internal.h
index c69bc5fa..f64dc626 100644
--- a/ssl/internal.h
+++ b/ssl/internal.h
@@ -919,7 +919,7 @@ int tls13_post_handshake(SSL *ssl);
  * it returns one. Otherwise, it sends an alert and returns zero. */
 int tls13_check_message_type(SSL *ssl, int type);
 
-int tls13_process_certificate(SSL *ssl);
+int tls13_process_certificate(SSL *ssl, int allow_anonymous);
 int tls13_process_certificate_verify(SSL *ssl);
 int tls13_process_finished(SSL *ssl);
 
diff --git a/ssl/test/runner/runner.go b/ssl/test/runner/runner.go
index 085d7e19..ee4694bc 100644
--- a/ssl/test/runner/runner.go
+++ b/ssl/test/runner/runner.go
@@ -1430,7 +1430,7 @@ func addBasicTests() {
 				},
 			},
 			shouldFail:    true,
-			expectedError: ":DECODE_ERROR:",
+			expectedError: ":PEER_DID_NOT_RETURN_A_CERTIFICATE:",
 		},
 		{
 			name:             "TLSFatalBadPackets",
diff --git a/ssl/tls13_both.c b/ssl/tls13_both.c
index dddc08e9..35fea53f 100644
--- a/ssl/tls13_both.c
+++ b/ssl/tls13_both.c
@@ -181,7 +181,7 @@ err:
   return 0;
 }
 
-int tls13_process_certificate(SSL *ssl) {
+int tls13_process_certificate(SSL *ssl, int allow_anonymous) {
   CBS cbs, context;
   CBS_init(&cbs, ssl->init_msg, ssl->init_num);
   if (!CBS_get_u8_length_prefixed(&cbs, &context) ||
@@ -191,12 +191,12 @@ int tls13_process_certificate(SSL *ssl) {
     return 0;
   }
 
+  const int retain_sha256 =
+      ssl->server && ssl->ctx->retain_only_sha256_of_client_certs;
   int ret = 0;
   uint8_t alert;
   STACK_OF(X509) *chain = ssl_parse_cert_chain(
-      ssl, &alert, ssl->ctx->retain_only_sha256_of_client_certs
-                       ? ssl->s3->new_session->peer_sha256
-                       : NULL,
+      ssl, &alert, retain_sha256 ? ssl->s3->new_session->peer_sha256 : NULL,
       &cbs);
   if (chain == NULL) {
     ssl3_send_alert(ssl, SSL3_AL_FATAL, alert);
@@ -210,15 +210,7 @@ int tls13_process_certificate(SSL *ssl) {
   }
 
   if (sk_X509_num(chain) == 0) {
-    /* Clients must receive a certificate from the server. */
-    if (!ssl->server) {
-      OPENSSL_PUT_ERROR(SSL, SSL_R_DECODE_ERROR);
-      ssl3_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_DECODE_ERROR);
-      goto err;
-    }
-
-    /* Servers may be configured to accept anonymous clients. */
-    if (ssl->verify_mode & SSL_VERIFY_FAIL_IF_NO_PEER_CERT) {
+    if (!allow_anonymous) {
       OPENSSL_PUT_ERROR(SSL, SSL_R_PEER_DID_NOT_RETURN_A_CERTIFICATE);
       ssl3_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_HANDSHAKE_FAILURE);
       goto err;
@@ -229,10 +221,7 @@ int tls13_process_certificate(SSL *ssl) {
     goto err;
   }
 
-  if (ssl->server && ssl->ctx->retain_only_sha256_of_client_certs) {
-    /* The hash was filled in by |ssl_parse_cert_chain|. */
-    ssl->s3->new_session->peer_sha256_valid = 1;
-  }
+  ssl->s3->new_session->peer_sha256_valid = retain_sha256;
 
   if (!ssl_verify_cert_chain(ssl, chain)) {
     goto err;
diff --git a/ssl/tls13_client.c b/ssl/tls13_client.c
index 376e0ac3..9dc49232 100644
--- a/ssl/tls13_client.c
+++ b/ssl/tls13_client.c
@@ -361,7 +361,7 @@ static enum ssl_hs_wait_t do_process_certificate_request(SSL *ssl,
 static enum ssl_hs_wait_t do_process_server_certificate(SSL *ssl,
                                                         SSL_HANDSHAKE *hs) {
   if (!tls13_check_message_type(ssl, SSL3_MT_CERTIFICATE) ||
-      !tls13_process_certificate(ssl) ||
+      !tls13_process_certificate(ssl, 0 /* certificate required */) ||
       !ssl->method->hash_current_message(ssl)) {
     return ssl_hs_error;
   }
diff --git a/ssl/tls13_server.c b/ssl/tls13_server.c
index 1b99ff6e..71c716d3 100644
--- a/ssl/tls13_server.c
+++ b/ssl/tls13_server.c
@@ -458,8 +458,11 @@ static enum ssl_hs_wait_t do_process_client_certificate(SSL *ssl,
     return ssl_hs_ok;
   }
 
+  const int allow_anonymous =
+      (ssl->verify_mode & SSL_VERIFY_FAIL_IF_NO_PEER_CERT) == 0;
+
   if (!tls13_check_message_type(ssl, SSL3_MT_CERTIFICATE) ||
-      !tls13_process_certificate(ssl) ||
+      !tls13_process_certificate(ssl, allow_anonymous) ||
       !ssl->method->hash_current_message(ssl)) {
     return ssl_hs_error;
   }