Should I log trivial fixes?

Question

I'm in a code shop of two. And while I understand that a bug tracker is useful where the number of programmers is greater or equal to one, I'm not so convinced that logging bugs, changes, and fixes is worth the time when they're trivial. When I find a simple bug, I understand it, fix it, and run it through some testing. And THEN I realized I need to go log it.

I know in theory that bug logging should be done somewhere between finding the bug and fixing the bug, but if fixing it is faster than logging it, it seems like a drag. In larger code-shops, the boss pays attention to who is doing what and it's nice to know where others are mucking about.

I find myself describing things that I've already fixed and then instantly closing them. I have doubts that anyone will ever look at this closed bug again. Is it time to trim the process fat?