"Can you cut me a deal?"
"May I have a discount?"
Ever had a client (or potential client) ask you a question such as these?
And, in response, "Sure, but may I cut the quality and value of my service?" To which I'm sure they'd reply, "No."
If a client won't accept a diminished value of service, why should you accept a cheaper payment?
Accept full payment; deliver quality service. Neither you nor your client should be satisfied with anything less. You're worth it and so is your client.