You could submit a range of prices...
Say something like: "£3 per square yard (Or whatever) would be the MAXIMUM we'd charge for a really dirty carpet. However, you'll probably pay far less. Our prices go as low as £1 per square yard, depending on how dirty the carpet is...etc"
That way, you are tempting the customer with the prospect of really low prices but aren't committing yourself to a fixed price.
You are also making it sound like you put work into making your prices as low as possible.
As an aside, shouldn't we all be quoting in metric these days? EU laws and what have you?