diff --git a/ssl/t1_lib.cc b/ssl/t1_lib.cc
index 678e4a3b..00c796ad 100644
--- a/ssl/t1_lib.cc
+++ b/ssl/t1_lib.cc
@@ -1038,7 +1038,6 @@ static bool ext_sigalgs_parse_clienthello(SSL_HANDSHAKE *hs, uint8_t *out_alert,
   CBS supported_signature_algorithms;
   if (!CBS_get_u16_length_prefixed(contents, &supported_signature_algorithms) ||
       CBS_len(contents) != 0 ||
-      CBS_len(&supported_signature_algorithms) == 0 ||
       !tls1_parse_peer_sigalgs(hs, &supported_signature_algorithms)) {
     return false;
   }
@@ -3556,7 +3555,10 @@ bool tls1_parse_peer_sigalgs(SSL_HANDSHAKE *hs, const CBS *in_sigalgs) {
     return true;
   }
 
-  return parse_u16_array(in_sigalgs, &hs->peer_sigalgs);
+  // In all contexts, the signature algorithms list may not be empty. (It may be
+  // omitted by clients in TLS 1.2, but then the entire extension is omitted.)
+  return CBS_len(in_sigalgs) != 0 &&
+         parse_u16_array(in_sigalgs, &hs->peer_sigalgs);
 }
 
 bool tls1_get_legacy_signature_algorithm(uint16_t *out, const EVP_PKEY *pkey) {
diff --git a/ssl/test/runner/runner.go b/ssl/test/runner/runner.go
index 6b251a27..da81f236 100644
--- a/ssl/test/runner/runner.go
+++ b/ssl/test/runner/runner.go
@@ -9306,26 +9306,8 @@ func addSignatureAlgorithmTests() {
 		expectedError: ":WRONG_SIGNATURE_TYPE:",
 	})
 
-	// Test that, if the list is missing, the peer falls back to SHA-1 in
-	// TLS 1.2, but not TLS 1.3.
-	testCases = append(testCases, testCase{
-		name: "ClientAuth-SHA1-Fallback-RSA",
-		config: Config{
-			MaxVersion: VersionTLS12,
-			ClientAuth: RequireAnyClientCert,
-			VerifySignatureAlgorithms: []signatureAlgorithm{
-				signatureRSAPKCS1WithSHA1,
-			},
-			Bugs: ProtocolBugs{
-				NoSignatureAlgorithms: true,
-			},
-		},
-		flags: []string{
-			"-cert-file", path.Join(*resourceDir, rsaCertificateFile),
-			"-key-file", path.Join(*resourceDir, rsaKeyFile),
-		},
-	})
-
+	// Test that, if the ClientHello list is missing, the server falls back
+	// to SHA-1 in TLS 1.2, but not TLS 1.3.
 	testCases = append(testCases, testCase{
 		testType: serverTest,
 		name:     "ServerAuth-SHA1-Fallback-RSA",
@@ -9344,24 +9326,6 @@ func addSignatureAlgorithmTests() {
 		},
 	})
 
-	testCases = append(testCases, testCase{
-		name: "ClientAuth-SHA1-Fallback-ECDSA",
-		config: Config{
-			MaxVersion: VersionTLS12,
-			ClientAuth: RequireAnyClientCert,
-			VerifySignatureAlgorithms: []signatureAlgorithm{
-				signatureECDSAWithSHA1,
-			},
-			Bugs: ProtocolBugs{
-				NoSignatureAlgorithms: true,
-			},
-		},
-		flags: []string{
-			"-cert-file", path.Join(*resourceDir, ecdsaP256CertificateFile),
-			"-key-file", path.Join(*resourceDir, ecdsaP256KeyFile),
-		},
-	})
-
 	testCases = append(testCases, testCase{
 		testType: serverTest,
 		name:     "ServerAuth-SHA1-Fallback-ECDSA",
@@ -9380,6 +9344,66 @@ func addSignatureAlgorithmTests() {
 		},
 	})
 
+	testCases = append(testCases, testCase{
+		testType: serverTest,
+		name:     "ServerAuth-NoFallback-TLS13",
+		config: Config{
+			MaxVersion: VersionTLS13,
+			VerifySignatureAlgorithms: []signatureAlgorithm{
+				signatureRSAPKCS1WithSHA1,
+			},
+			Bugs: ProtocolBugs{
+				NoSignatureAlgorithms: true,
+			},
+		},
+		shouldFail:    true,
+		expectedError: ":NO_COMMON_SIGNATURE_ALGORITHMS:",
+	})
+
+	// The CertificateRequest list, however, may never be omitted. It is a
+	// syntax error for it to be empty.
+	testCases = append(testCases, testCase{
+		name: "ClientAuth-NoFallback-RSA",
+		config: Config{
+			MaxVersion: VersionTLS12,
+			ClientAuth: RequireAnyClientCert,
+			VerifySignatureAlgorithms: []signatureAlgorithm{
+				signatureRSAPKCS1WithSHA1,
+			},
+			Bugs: ProtocolBugs{
+				NoSignatureAlgorithms: true,
+			},
+		},
+		flags: []string{
+			"-cert-file", path.Join(*resourceDir, rsaCertificateFile),
+			"-key-file", path.Join(*resourceDir, rsaKeyFile),
+		},
+		shouldFail:         true,
+		expectedError:      ":DECODE_ERROR:",
+		expectedLocalError: "remote error: error decoding message",
+	})
+
+	testCases = append(testCases, testCase{
+		name: "ClientAuth-NoFallback-ECDSA",
+		config: Config{
+			MaxVersion: VersionTLS12,
+			ClientAuth: RequireAnyClientCert,
+			VerifySignatureAlgorithms: []signatureAlgorithm{
+				signatureECDSAWithSHA1,
+			},
+			Bugs: ProtocolBugs{
+				NoSignatureAlgorithms: true,
+			},
+		},
+		flags: []string{
+			"-cert-file", path.Join(*resourceDir, ecdsaP256CertificateFile),
+			"-key-file", path.Join(*resourceDir, ecdsaP256KeyFile),
+		},
+		shouldFail:         true,
+		expectedError:      ":DECODE_ERROR:",
+		expectedLocalError: "remote error: error decoding message",
+	})
+
 	testCases = append(testCases, testCase{
 		name: "ClientAuth-NoFallback-TLS13",
 		config: Config{
@@ -9396,29 +9420,11 @@ func addSignatureAlgorithmTests() {
 			"-cert-file", path.Join(*resourceDir, rsaCertificateFile),
 			"-key-file", path.Join(*resourceDir, rsaKeyFile),
 		},
-		shouldFail: true,
-		// An empty CertificateRequest signature algorithm list is a
-		// syntax error in TLS 1.3.
+		shouldFail:         true,
 		expectedError:      ":DECODE_ERROR:",
 		expectedLocalError: "remote error: error decoding message",
 	})
 
-	testCases = append(testCases, testCase{
-		testType: serverTest,
-		name:     "ServerAuth-NoFallback-TLS13",
-		config: Config{
-			MaxVersion: VersionTLS13,
-			VerifySignatureAlgorithms: []signatureAlgorithm{
-				signatureRSAPKCS1WithSHA1,
-			},
-			Bugs: ProtocolBugs{
-				NoSignatureAlgorithms: true,
-			},
-		},
-		shouldFail:    true,
-		expectedError: ":NO_COMMON_SIGNATURE_ALGORITHMS:",
-	})
-
 	// Test that signature preferences are enforced. BoringSSL does not
 	// implement MD5 signatures.
 	testCases = append(testCases, testCase{
diff --git a/ssl/tls13_client.cc b/ssl/tls13_client.cc
index 0d3e8771..0d778962 100644
--- a/ssl/tls13_client.cc
+++ b/ssl/tls13_client.cc
@@ -506,7 +506,6 @@ static enum ssl_hs_wait_t do_read_certificate_request(SSL_HANDSHAKE *hs) {
       !have_sigalgs ||
       !CBS_get_u16_length_prefixed(&sigalgs,
                                    &supported_signature_algorithms) ||
-      CBS_len(&supported_signature_algorithms) == 0 ||
       !tls1_parse_peer_sigalgs(hs, &supported_signature_algorithms)) {
     ssl_send_alert(ssl, SSL3_AL_FATAL, alert);
     OPENSSL_PUT_ERROR(SSL, SSL_R_DECODE_ERROR);