Anchoring is a different effect than you might have thought. In breakthrough research, it was shown that when people were asked to write down completely random numbers (such as the last four digits of their social security number), before taking a guess at the value of a home (say; might have been something else), it had an absurdly strong effect on the value of their guesses. (People with coincidentally high last-four-digits wrote much, much higher ones than people with coincidentally low last-four-digits, even though it's obvious they wouldn't have even thought twice about it. If I asked you to think about the last four digits of your social security number, what that happened to be would impact any other valuation you were making immediately after.

The mere mention of a number - any number - "anchors" psychologically in an absurdly strong way.

So in that sense, the statement: "I offered a fixed-price 'no win, no fee' rate" includes the literal mention (like the social security ending digits 0000) of "no fee" -- so it doesn't matter what the sentence is. The sentence could read "Obviously I wouldn't be able to do it for no fee" and it would anchor to $0, whereas, if you said, "I obviously wouldn't charge a hundred billion dollars" it will anchor it to a hundred billion dollars.

These effects are incredibly bizarre. I'm not an expert salesperson but I do know about them.

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I guess I should give a reference: http://www.nytimes.com/2011/11/27/books/review/thinking-fast...

Is a good introductory article. Daniel Kahneman is the name most associated with this research, or at least reporting it, and he won a Nobel prize* in Economics in 2002 for his work.

* (the Nobel Memorial Prize in Economic Sciences by the Swedish National Bank)