I just discovered a great way to harmonize the demands of plot and character: sit the character under a bright light and ask, "Why did you kill Mrs. Johnson?"
Equally valid questions include, "Why are you an uptight jerk," "Why so glum," and "Who crapped in your pancakes?"
When I think of a story, I always know the plot before the characters. That means that my characters are initially designed as place-holders. But if I want the story to be compelling, they've got to be more than that: they've got to be the actual creatures driving the story forward, rather than the other way around.
I realized this when I was trying to cram my protagonist into the main "twist" of my novel-in-progress--which is, simply put: a side-character disappears, and the protagonist is paralyzed by her absence. The twist didn't fit with the character, though, because there was no clear reason why the loss of this side-character would cause his breakdown.
When I finally put him under the interrogation light and asked why he broke down--why it was he couldn't go on without that side-character (that brilliant, unerringly wise sidekick of his)--I realized that the only answer my protagonist could give me was: "I'm stupid."
That's going to call for some changes to the way the protagonist acts; he's said some rather clever things in the past. But those changes won't be radical, and they'll make him significantly deeper. But most importantly, what I consider to be the ingenious plot--which is what got me writing the story in the first place--will be saved.