When in a contract you want to specify a fee to be paid, it’s redundant to use the phrase flat fee or fixed fee:
The Bank agrees to pay RP Financial
a fixed fee of$37,500 for preparation and delivery of the original appraisal report, plus reimbursable expenses.
During the Term, DigitalGlobe shall pay Consultant
a fixed fee of$10,000 per month for up to 15 hours per month of Consultant’s time (“Fee”).
For Services rendered by Consultant under this Agreement, the Company shall pay Consultant
a flat fee of$ 4,000 per month.
The Contractor will also be paid
a flat fee of$1,500 for his participation and support of our Independent Auditors during their field work in China and for the representation of the Company at the Rodman Renshaw conference in China that will take place in March , 2011.
Those phrases make sense only when you’re referring generically to a kind of payment, rather than a specific fee:
Such fee, at Landlord’s option, shall be either a fixed fee or a fee calculated an hourly basis considering the time expended by Landlord’s agents or representatives in supervising Tenant’s construction.
Wherever possible, the charge will be a flat fee.
I suppose that if circumstances are such that the reader might think that the payment is a recurring one, you could use one-time payment. But I can’t offhand think of any such scenario.
(By the way, the above extracts are fresh from EDGAR—I don’t endorse the drafting in any of them.)
[Updated October 31, 2011: The same could be said about references to payment of “a lump-sum” of $X.]