Reading the playtest PDF, I noticed that the Operative's Overwhelming Strike ability (p89) can cause three different debuffs. Two of them are standard conditions but the third is "The target can’t Take Cover or benefit from cover." What would people think of replacing it with a new standard condition, perhaps called Exposed, which either steps down the target's level of cover or just negates it entirely. This then frees it up to be caused by other effects, such as sniping from elevation or damaging cover with a heavy weapon.
By default, I would suggest you get rid of Exposed by using the Take Cover action again or moving into a different piece of cover, though of course Overwhelming Strike would prevent you from getting rid of the condition until the end of the operative's next turn. Generally, this would be one of those conditions that applies to specific enemies, like how flanking makes you off-guard only to the folks flanking you. That way they can keep their current cover benefits against everyone except the one who made them Exposed.
Flavour-wise, I would describe it as something like "The cover you are relying on is ineffective at protecting you from incoming attacks. You gain no benefits from cover until you either use the Take Cover action again or move into a different piece of cover."
What do folks think? I should add that I have only been reading the PDF and haven't had a chance to play yet.