In the bounty system FAQ it states that...
Can I offer a second bounty after the first one has expired?
Note that if you offer several bounties on the same question, you will have to double the amount each time (or more). That is, if your first bounty was worth 50 reputation, your second bounty on the same question will have to be for at least 100, your third for at least 200 and so on. If you've already offered a bounty for more than 250, you can still offer more bounties for 500 (the maximum amount) as long as you like (or as long as you have the rep). This doubling applies only to bounties by the same user on the same question.
I recently asked a question, offered a 100 rep bounty to raise visibility and had 2 answers that I'd like to show some love for. One of them is easy - I just awarded the bounty and accepted it because it was the most useful.
I had planned to just start a second bounty for 50 rep and award that to the second answer because it was also useful for another aspect of the solution, it just wasn't the most helpful. Of course, after trying that I found that I can only award 200-rep or more, which I don't want to do because the accepted answer who helped the most only got 125 (accept for 15, upvote for 10 plus the bounty).
I actually considered accepting the second-most-useful answer to give him 25 rep (upvote for 10, accept for 15) then bountying the most useful answer for a total of 110 rep, even though I know full well that's absolutely not the way SE wants me to do it.
Is there a good reason why I can't award a lower-value bounty, and if so, is there any way to appreciate the useful answer more than just a +10 rep?