How to set padding for signed key encryption in java?

Question

// cipher = Cipher.getInstance("RSA/ECB/PKCS1Padding");

 public byte[] sign_and_encrypt( SecretKey key ) throws InvalidKeyException, IllegalBlockSizeException, BadPaddingException {
        cipher.init(Cipher.WRAP_MODE, priv_key);
        byte [] signed = cipher.wrap(key);

        cipher.init(Cipher.ENCRYPT_MODE, their_pub_key);
        System.out.println("Signed length: " + signed.length);

        return cipher.doFinal(signed);
 }

I'm having an issue signing and encrypting a session key in java. byte[] signed is 256 bytes in length, but the doFinal at the bottom can only take blocks of size 245 or less.

Is there a way to set the amount of padding added? Or another way to get this working without encrypting two slices of signed?

The exception I'm getting is

javax.crypto.IllegalBlockSizeException: Data must not be longer than 245 bytes
    at com.sun.crypto.provider.RSACipher.doFinal(RSACipher.java:344)
    at com.sun.crypto.provider.RSACipher.engineDoFinal(RSACipher.java:389)
    at javax.crypto.Cipher.doFinal(Cipher.java:2165)
    at Crypto.JEncrypRSA.sign_and_encrypt(JEncrypRSA.java:76)
    at Chat.Client.get_session_key(Client.java:115)
    at Chat.Client.main(Client.java:131)