Mysteries of mystery writing

All right, real mystery writers: how do you do it?

By "it," I mean figuring out the plot--all the details of who did it, why, who knows what, and who believes what. Most of all, I'm wondering when you figure all that out. Do you map it all out at the beginning or do you figure it out in the course of the writing? Or does it vary from writer to writer (as do pretty much all aspects of writing)?

I ask because I think the culprit in my literary murder mystery is about to change for the third time. In this case it really seems like the story itself is pointing to this person, whom I, like my protagonist, had dismissed out of hand. It's been an interesting experience to observe this happening, as I had certain characters arguing for this person's guilt, and it's as if they finally convinced me. The change, should I choose to implement it, also allows my protagonist to be productively wrong, rather than just sadly misunderstood (fortunately he's not a heroic detective, just a sort of hapless bystander who decides to get involved).

However, questions remain: If the story itself is insisting on this particular culprit, maybe the culprit is too obvious. Maybe the reader will grow fed up with the protagonist's seemingly willful blindness early on. OR will the case the protagonist is building against someone else be enough to raise doubts in the reader's mind? Also, does the culprit always have to be a mystery until the end, or, in the manner of the old Columbo mysteries, can the interest lie less in who the person is than in how he or she is discovered? (The fact that Columbo is my touchstone for such questions should tell you that I know relatively little about the mystery genre, which is part of my problem.) And, also, in a novel that aims for literary interest, is the whodunnit aspect even that important?

I find that even in my "purely" literary writing I suffer from plot anxiety. I worry that the story is simply too boring, that nothing is happening, and so if anything I over-plot. In an actual mystery story, a convoluted plot can, I think, be satisfying, as long as it doesn't seem contrived. But there's a fine line between convoluted and contrived. And then there's the kind of story, which I'm ultimately working toward, in which we don't get a final answer. In the end, different characters are still going to believe different things, and there won't be enough evidence to convict the apparent killer. However, I still think I need to have a firm notion of the culprit in my mind in order to write this kind of story, and then think of ways he could be overlooked by others.

In a way, I suppose, all fiction writing is mystery writing of a sort: What's going to happen? What will be revealed? Who is this character, really?

So I guess the answer, as always, is to keep writing and then get someone honest to read it and tear it apart. Still, I would love to know how people who think up mystery stories for a living really do it.