I've been using the idea of anti-expertise, or maybe flaws (I haven't worked out a good name). Basically, it is an aspect of a skill, like existing skill concentrations, that works against you rather than for you. Just like adding an expertise die when the task would logically be covered by a specialization, it would remove one when it would logically be covered by a flaw. A character might for example have a flaw in hearing on Wisdom (Perception) rolls, such that any such roll involving sound would subtract 1d4 from the total roll. A PC may take up to two flaws at character creation, choosing from the same categories as skill concentrations. Succeeding on a skill roll that features a flaw earns the PC Inspiration in the same way that one earns it from various tasks related to the PC's Destiny.