We give a general approach to characterizing minimal information in a modal context. Our modal treatment can be used for many applications, but is especially relevant under epistemic interpretations of an operator. Relative to a modal system S, we give three characterizations of minimality of a formula ϕ and give conditions under which these characterizations are equivalent. We then argue that rather than using bisimulations, it is more appropriate to base information orders on Ehrenfeucht-Fraïssé games to come up with a satisfactory analysis of minimality. Moving to the realm of epistemic logics, we show that for one of these information orders almost all systems trivialize, i.e., either all or no formulas are honest. The other order is much more promising as it permits to minimize wrt positive knowledge. The resulting notion of minimality coincides with well-established accounts of minimal knowledge in S5. For S4 we compare the two orders.