You can end up paying more for the same services even with a rate freeze in place

You can’t declare “mission accomplished” when your law firms agree to freeze their billing rates. The reason you can’t is that firms may end up with more senior lawyer time on similar matters than before the rates froze. In fact, that shift upward may be likely since for the same reason you have tightened the belt – budget constraints due to business falloff — at the law firm work may be less plentiful. The senior lawyers hoard work to plump up their own chargeable hours and handle more of the work at their higher, albeit frozen, rates. True, rates did not go up; false, fees held even or declined.