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One of the things I tinker with most from one draft to the next of my trilogy is how many characters to include. I don't want to have characters in there who serve no function, but I also don't want to pare it down so much that mysteries are given away by process of elimination. Then there's the character whose first appearance has been bumped back so often that her original appearance in book one has moved to book three.
Just because a character appears, it doesn't mean that character should get his or her own perspective. But characters do need to serve some purpose, or they're just set dressing. It needn't be an essential function, though I recommend that, if your characters are important enough to appear in your story, they're also important enough to have their own motivations, choices, and lives outside the protagonist.
Making well-rounded characters who can carry the story isn't my problem. At least, if it is, my writing group hasn't mentioned it. My problem is that I often don't know what to do with people, or I lose track of them.
Fortunately, I do have a couple of backup plans for things to do with characters who I don't want to toss into the climax of the story. First, I might use them to highlight a feature I want to show about my main character. For instance, I had trouble figuring out what purpose my protagonist's friend-and-roommate served. Then I made her more trusting and open to contrast against my protagonist's closed-off, mistrusting nature, which made it a lot more obvious without telling the reader all about it.
Second, I can use my useless side characters to point something out instead of wallowing in introspection and navel-gazing. Listening to characters talk to themselves is boring, but, as dialogue, it's more interesting. Revelations that might take pages and pages of thought process for one character may be a one-off remark for another. One of the major problems with pacing in the first book in my trilogy was solved by adding a second perspective. Then I didn't have to wait for that character to get around to telling my protagonist what was going on; he shared it with the reader in his own sections, and the story moved briskly along.
If your side characters are warping or taking over the story, you may want to consider tabling that side plot for another book. But each character should serve a purpose, just as every scene, every interaction, every description, also serves it.
You can always add or subtract characters as you need to. I recommend that you play around with this, until you've found the right balance and hit upon just the right number. I can't tell you what that exact number will be, though. That would make it easy, and since when has writing been easy?
Generally speaking, though, three or fewer characters are good for short stories, but novels need more.