diff --git a/common.go b/common.go
index 4b8e023..8011ceb 100644
--- a/common.go
+++ b/common.go
@@ -5,6 +5,7 @@
 package tls
 
 import (
+	"bytes"
 	"container/list"
 	"crypto"
 	"crypto/ecdsa"
@@ -407,6 +408,9 @@ type CertificateRequestInfo struct {
 	// SignatureSchemes lists the signature schemes that the server is
 	// willing to verify.
 	SignatureSchemes []SignatureScheme
+
+	// Version is the TLS version that was negotiated for this connection.
+	Version uint16
 }
 
 // RenegotiationSupport enumerates the different levels of support for TLS
@@ -1070,6 +1074,38 @@ func (chi *ClientHelloInfo) SupportsCertificate(c *Certificate) error {
 	return nil
 }
 
+// SupportsCertificate returns nil if the provided certificate is supported by
+// the server that sent the CertificateRequest. Otherwise, it returns an error
+// describing the reason for the incompatibility.
+func (cri *CertificateRequestInfo) SupportsCertificate(c *Certificate) error {
+	if _, err := selectSignatureScheme(cri.Version, c, cri.SignatureSchemes); err != nil {
+		return err
+	}
+
+	if len(cri.AcceptableCAs) == 0 {
+		return nil
+	}
+
+	for j, cert := range c.Certificate {
+		x509Cert := c.Leaf
+		// Parse the certificate if this isn't the leaf node, or if
+		// chain.Leaf was nil.
+		if j != 0 || x509Cert == nil {
+			var err error
+			if x509Cert, err = x509.ParseCertificate(cert); err != nil {
+				return fmt.Errorf("failed to parse certificate #%d in the chain: %w", j, err)
+			}
+		}
+
+		for _, ca := range cri.AcceptableCAs {
+			if bytes.Equal(x509Cert.RawIssuer, ca) {
+				return nil
+			}
+		}
+	}
+	return errors.New("chain is not signed by an acceptable CA")
+}
+
 // BuildNameToCertificate parses c.Certificates and builds c.NameToCertificate
 // from the CommonName and SubjectAlternateName fields of each of the leaf
 // certificates.
diff --git a/handshake_client.go b/handshake_client.go
index 989df76..4fb528c 100644
--- a/handshake_client.go
+++ b/handshake_client.go
@@ -16,7 +16,6 @@ import (
 	"fmt"
 	"io"
 	"net"
-	"strconv"
 	"strings"
 	"sync/atomic"
 	"time"
@@ -518,7 +517,7 @@ func (hs *clientHandshakeState) doFullHandshake() error {
 		certRequested = true
 		hs.finishedHash.Write(certReq.marshal())
 
-		cri := certificateRequestInfoFromMsg(certReq)
+		cri := certificateRequestInfoFromMsg(c.vers, certReq)
 		if chainToSend, err = c.getClientCertificate(cri); err != nil {
 			c.sendAlert(alertInternalError)
 			return err
@@ -850,7 +849,12 @@ var (
 
 // certificateRequestInfoFromMsg generates a CertificateRequestInfo from a TLS
 // <= 1.2 CertificateRequest, making an effort to fill in missing information.
-func certificateRequestInfoFromMsg(certReq *certificateRequestMsg) *CertificateRequestInfo {
+func certificateRequestInfoFromMsg(vers uint16, certReq *certificateRequestMsg) *CertificateRequestInfo {
+	cri := &CertificateRequestInfo{
+		AcceptableCAs: certReq.certificateAuthorities,
+		Version:       vers,
+	}
+
 	var rsaAvail, ecAvail bool
 	for _, certType := range certReq.certificateTypes {
 		switch certType {
@@ -861,10 +865,6 @@ func certificateRequestInfoFromMsg(certReq *certificateRequestMsg) *CertificateR
 		}
 	}
 
-	cri := &CertificateRequestInfo{
-		AcceptableCAs: certReq.certificateAuthorities,
-	}
-
 	if !certReq.hasSignatureAlgorithm {
 		// Prior to TLS 1.2, the signature schemes were not
 		// included in the certificate request message. In this
@@ -909,43 +909,11 @@ func (c *Conn) getClientCertificate(cri *CertificateRequestInfo) (*Certificate,
 		return c.config.GetClientCertificate(cri)
 	}
 
-	// We need to search our list of client certs for one
-	// where SignatureAlgorithm is acceptable to the server and the
-	// Issuer is in AcceptableCAs.
-	for i, chain := range c.config.Certificates {
-		sigOK := false
-		for _, alg := range signatureSchemesForCertificate(c.vers, &chain) {
-			if isSupportedSignatureAlgorithm(alg, cri.SignatureSchemes) {
-				sigOK = true
-				break
-			}
-		}
-		if !sigOK {
+	for _, chain := range c.config.Certificates {
+		if err := cri.SupportsCertificate(&chain); err != nil {
 			continue
 		}
-
-		if len(cri.AcceptableCAs) == 0 {
-			return &chain, nil
-		}
-
-		for j, cert := range chain.Certificate {
-			x509Cert := chain.Leaf
-			// Parse the certificate if this isn't the leaf node, or if
-			// chain.Leaf was nil.
-			if j != 0 || x509Cert == nil {
-				var err error
-				if x509Cert, err = x509.ParseCertificate(cert); err != nil {
-					c.sendAlert(alertInternalError)
-					return nil, errors.New("tls: failed to parse configured certificate chain #" + strconv.Itoa(i) + ": " + err.Error())
-				}
-			}
-
-			for _, ca := range cri.AcceptableCAs {
-				if bytes.Equal(x509Cert.RawIssuer, ca) {
-					return &chain, nil
-				}
-			}
-		}
+		return &chain, nil
 	}
 
 	// No acceptable certificate found. Don't send a certificate.
diff --git a/handshake_client_tls13.go b/handshake_client_tls13.go
index 66775ff..8994591 100644
--- a/handshake_client_tls13.go
+++ b/handshake_client_tls13.go
@@ -526,6 +526,7 @@ func (hs *clientHandshakeStateTLS13) sendClientCertificate() error {
 	cert, err := c.getClientCertificate(&CertificateRequestInfo{
 		AcceptableCAs:    hs.certReq.certificateAuthorities,
 		SignatureSchemes: hs.certReq.supportedSignatureAlgorithms,
+		Version:          c.vers,
 	})
 	if err != nil {
 		return err