Cheque discounting is same as cheque purchase. A/c payee cheque cannot be endorsed in favor of anyone else. If there is no branch of the bank's cheque that you have received, you can take it to some other bank in which your account exists and ask the branch to purchase it. The charges will be more for purchasing cheque than collecting it on your behalf. The advantage is you will get money the day your cheque is given to bank for purchase. People who want money quickly without waiting for proceeds of cheque to realize use this option even at the loss of some greater amount of charges to be paid to bank. It depends on your goodwill with the bank where your account is maintained. The bank is at risk because if the cheque is returned unpaid, it should be able to recover the cheque amount from you. Hence banker will study your credibility before purchasing the cheque. If it is a banker's cheque, Demand draft or Pay order the banker does not hesitate at all to purchase it at once. Only if it is cheque issued by individual or any company/firm, banker will study your profile a bit to assess the risk of return and when he confirms that your profile is good enough to recover dues if cheque is returned then only he will purchase the cheque.
But third party cannot utilize the option of giving it to some bank and get it discounted because it is account payee cheque. Third party can utilize the option of cheque discount if it is not an account payee cheque and also if it is endorsed by the payee on its behalf.