A $1 discount is ~0.1% of an $800/day bill rate.

A $1 discount is ~0.025% of a $4000/week bill rate.

A $1 discount is ~0.001% of an $8000 project.

In what increment do you want to negotiate your rate? In full percentage points, or in hundredths of a percent?

And what figures do you want to be negotiating in: amounts that are low enough that your client can immediately get their heads around, like $100 vs. $150, or the real amounts their company will pay in the end, like $8000 vs. $7900, where an individual person at the company is less likely to feel like they should have a strong opinion?

Remember this: your clients are not paying you with their own money. It is monopoly money to them. It comes out of a budget, not their own pockets.

(To say nothing of the fact that when you bill hourly, you give your clients tacit permission to ask for your time in hourly increments).