diff --git a/common.go b/common.go
index 584a361..ec3e997 100644
--- a/common.go
+++ b/common.go
@@ -489,10 +489,10 @@ func (c *Config) BuildNameToCertificate() {
 type Certificate struct {
 	Certificate [][]byte
 	// PrivateKey contains the private key corresponding to the public key
-	// in Leaf. For a server, this must be a *rsa.PrivateKey or
-	// *ecdsa.PrivateKey. For a client doing client authentication, this
-	// can be any type that implements crypto.Signer (which includes RSA
-	// and ECDSA private keys).
+	// in Leaf. For a server, this must implement either crypto.Decrypter
+	// (implemented by RSA private keys) or crypto.Signer (which includes
+	// RSA and ECDSA private keys). For a client doing client authentication,
+	// this can be any type that implements crypto.Signer.
 	PrivateKey crypto.PrivateKey
 	// OCSPStaple contains an optional OCSP response which will be served
 	// to clients that request it.
diff --git a/handshake_server.go b/handshake_server.go
index c7c1f1e..8b31c7c 100644
--- a/handshake_server.go
+++ b/handshake_server.go
@@ -25,6 +25,9 @@ type serverHandshakeState struct {
 	suite           *cipherSuite
 	ellipticOk      bool
 	ecdsaOk         bool
+	rsaOk           bool
+	signOk          bool
+	decryptOk       bool
 	sessionState    *sessionState
 	finishedHash    finishedHash
 	masterSecret    []byte
@@ -197,7 +200,28 @@ Curves:
 		}
 	}
 
-	_, hs.ecdsaOk = hs.cert.PrivateKey.(*ecdsa.PrivateKey)
+	if priv, ok := hs.cert.PrivateKey.(crypto.Signer); ok {
+		hs.signOk = true
+		switch priv.Public().(type) {
+		case *ecdsa.PublicKey:
+			hs.ecdsaOk = true
+		case *rsa.PublicKey:
+			hs.rsaOk = true
+		default:
+			c.sendAlert(alertInternalError)
+			return false, fmt.Errorf("crypto/tls: unsupported signing key type (%T)", priv.Public())
+		}
+	}
+	if priv, ok := hs.cert.PrivateKey.(crypto.Decrypter); ok {
+		hs.decryptOk = true
+		switch priv.Public().(type) {
+		case *rsa.PublicKey:
+			hs.rsaOk = true
+		default:
+			c.sendAlert(alertInternalError)
+			return false, fmt.Errorf("crypto/tls: unsupported decryption key type (%T)", priv.Public())
+		}
+	}
 
 	if hs.checkForResumption() {
 		return true, nil
@@ -213,7 +237,7 @@ Curves:
 	}
 
 	for _, id := range preferenceList {
-		if hs.suite = c.tryCipherSuite(id, supportedList, c.vers, hs.ellipticOk, hs.ecdsaOk); hs.suite != nil {
+		if hs.setCipherSuite(id, supportedList, c.vers) {
 			break
 		}
 	}
@@ -272,8 +296,7 @@ func (hs *serverHandshakeState) checkForResumption() bool {
 	}
 
 	// Check that we also support the ciphersuite from the session.
-	hs.suite = c.tryCipherSuite(hs.sessionState.cipherSuite, c.config.cipherSuites(), hs.sessionState.vers, hs.ellipticOk, hs.ecdsaOk)
-	if hs.suite == nil {
+	if !hs.setCipherSuite(hs.sessionState.cipherSuite, c.config.cipherSuites(), hs.sessionState.vers) {
 		return false
 	}
 
@@ -649,9 +672,10 @@ func (hs *serverHandshakeState) processCertsFromClient(certificates [][]byte) (c
 	return nil, nil
 }
 
-// tryCipherSuite returns a cipherSuite with the given id if that cipher suite
-// is acceptable to use.
-func (c *Conn) tryCipherSuite(id uint16, supportedCipherSuites []uint16, version uint16, ellipticOk, ecdsaOk bool) *cipherSuite {
+// setCipherSuite sets a cipherSuite with the given id as the serverHandshakeState
+// suite if that cipher suite is acceptable to use.
+// It returns a bool indicating if the suite was set.
+func (hs *serverHandshakeState) setCipherSuite(id uint16, supportedCipherSuites []uint16, version uint16) bool {
 	for _, supported := range supportedCipherSuites {
 		if id == supported {
 			var candidate *cipherSuite
@@ -667,18 +691,26 @@ func (c *Conn) tryCipherSuite(id uint16, supportedCipherSuites []uint16, version
 			}
 			// Don't select a ciphersuite which we can't
 			// support for this client.
-			if (candidate.flags&suiteECDHE != 0) && !ellipticOk {
-				continue
-			}
-			if (candidate.flags&suiteECDSA != 0) != ecdsaOk {
+			if candidate.flags&suiteECDHE != 0 {
+				if !hs.ellipticOk || !hs.signOk {
+					continue
+				}
+				if candidate.flags&suiteECDSA != 0 {
+					if !hs.ecdsaOk {
+						continue
+					}
+				} else if !hs.rsaOk {
+					continue
+				}
+			} else if !hs.decryptOk || !hs.rsaOk {
 				continue
 			}
 			if version < VersionTLS12 && candidate.flags&suiteTLS12 != 0 {
 				continue
 			}
-			return candidate
+			hs.suite = candidate
+			return true
 		}
 	}
-
-	return nil
+	return false
 }
diff --git a/key_agreement.go b/key_agreement.go
index 0974fc6..d57d933 100644
--- a/key_agreement.go
+++ b/key_agreement.go
@@ -31,12 +31,6 @@ func (ka rsaKeyAgreement) generateServerKeyExchange(config *Config, cert *Certif
 }
 
 func (ka rsaKeyAgreement) processClientKeyExchange(config *Config, cert *Certificate, ckx *clientKeyExchangeMsg, version uint16) ([]byte, error) {
-	preMasterSecret := make([]byte, 48)
-	_, err := io.ReadFull(config.rand(), preMasterSecret[2:])
-	if err != nil {
-		return nil, err
-	}
-
 	if len(ckx.ciphertext) < 2 {
 		return nil, errClientKeyExchange
 	}
@@ -49,8 +43,12 @@ func (ka rsaKeyAgreement) processClientKeyExchange(config *Config, cert *Certifi
 		}
 		ciphertext = ckx.ciphertext[2:]
 	}
-
-	err = rsa.DecryptPKCS1v15SessionKey(config.rand(), cert.PrivateKey.(*rsa.PrivateKey), ciphertext, preMasterSecret)
+	priv, ok := cert.PrivateKey.(crypto.Decrypter)
+	if !ok {
+		return nil, errors.New("tls: certificate private key does not implement crypto.Decrypter")
+	}
+	// Perform contant time RSA PKCS#1 v1.5 decryption
+	preMasterSecret, err := priv.Decrypt(config.rand(), ciphertext, &rsa.PKCS1v15DecryptOptions{SessionKeyLen: 48})
 	if err != nil {
 		return nil, err
 	}
@@ -239,30 +237,30 @@ NextCandidate:
 	if err != nil {
 		return nil, err
 	}
+
+	priv, ok := cert.PrivateKey.(crypto.Signer)
+	if !ok {
+		return nil, errors.New("tls: certificate private key does not implement crypto.Signer")
+	}
 	var sig []byte
 	switch ka.sigType {
 	case signatureECDSA:
-		privKey, ok := cert.PrivateKey.(*ecdsa.PrivateKey)
+		_, ok := priv.Public().(*ecdsa.PublicKey)
 		if !ok {
-			return nil, errors.New("ECDHE ECDSA requires an ECDSA server private key")
+			return nil, errors.New("ECDHE ECDSA requires an ECDSA server key")
 		}
-		r, s, err := ecdsa.Sign(config.rand(), privKey, digest)
-		if err != nil {
-			return nil, errors.New("failed to sign ECDHE parameters: " + err.Error())
-		}
-		sig, err = asn1.Marshal(ecdsaSignature{r, s})
 	case signatureRSA:
-		privKey, ok := cert.PrivateKey.(*rsa.PrivateKey)
+		_, ok := priv.Public().(*rsa.PublicKey)
 		if !ok {
-			return nil, errors.New("ECDHE RSA requires a RSA server private key")
-		}
-		sig, err = rsa.SignPKCS1v15(config.rand(), privKey, hashFunc, digest)
-		if err != nil {
-			return nil, errors.New("failed to sign ECDHE parameters: " + err.Error())
+			return nil, errors.New("ECDHE RSA requires a RSA server key")
 		}
 	default:
 		return nil, errors.New("unknown ECDHE signature algorithm")
 	}
+	sig, err = priv.Sign(config.rand(), digest, hashFunc)
+	if err != nil {
+		return nil, errors.New("failed to sign ECDHE parameters: " + err.Error())
+	}
 
 	skx := new(serverKeyExchangeMsg)
 	sigAndHashLen := 0