All attorney fees are negotiable. In other words, you can always ask for the 20% fee. But keep in mind, the cheapest lawyer isn’t necessarily the best lawyer. If the best traumatic brain injury lawyer in town has a fee structure that you don’t like, it may be worth accepting it because he is going to get you a bigger settlement than someone with less of a reputation.
Another thing to keep in mind is that the vast majority of cases never go to trial; so, accepting this kind of fee agreement may be a good gamble.
A fee agreement that has an increasing fee percentage may work in your favor. If the percentage gets higher at trial, your attorney may bypass a low first settlement offer because he has an incentive to see the case to whatever end is appropriate – which may just be a trial.