Related tangent: I wish "AMAP" (as much as possible) would catch on, too.

ASAP, to my ears, always connotes urgency, and I'd even go so far as to say that its usage without this sense is universally dispreferred, if not outright misusage. Or at least I used to think so ... until a misunderstanding arose because our CEO did, in fact, use it in such a way (i.e. "whenever you are able").

H. Paul Grice (the four maxims guy) calls connotations like these implicatures, extra propositions which are "implicated" (implied) in addition to "what is said" (the utterance), and they can be conversational or conventional. Conversational implicatures are cancellable, meaning that they can be disavowed, whereas conventional implicatures cannot. So for instance, "I used to do a lot of drugs. I still do, but I used to too" cancels the implicature which arises from "used to" ("not anymore"). After consistent usage, however, conversational implicatures may become conventional and cannot be cancelled - they have moved from the pragmatic level to the semantic level (i.e. they're part of the meaning of the utterance itself rather than derived contextually).

The point being, is it even possible to cancel the urgency connotation of ASAP? Is it not just outright weird to say, "I want these TPS reports done ASAP - but no rush"?

My intuition says that ASAP necessarily connotes urgency, due to its consistent usage in this sense, whereas "as soon as possible" only optionally does (so it's much more acceptable to say, "I want these GPS reports done as soon as possible - but no rush").

Super weird coming from our CEO, because otherwise everything is in fact urgent (sigh...).