  We introduce a refinement of the usual Ehrenfeucht-Fra\"{\i}ss\'e game. The
new game will help us make finer distinctions than the traditional one. In
particular, it can be used to measure the size formulas needed for expressing a
given property. We will give two versions of the game: the first version
characterizes the size of formulas in propositional logic, and the second
version works for first-order predicate logic.
