I've been trying to get better with my flash. One thing I've learned is that you can use the exposure bias together with the flash bias to control what light comes from where. Basically, exposure bias controls the background and flash bias controls the foreground.
I figured this out while I was shooting a band on stage one night. I noticed that my flash was blowing away all of the stage lighting, but without the flash, I couldn't see any faces (the stage lights were mostly behind the musicians). So, I put +1 stop on the exposure bias, and -1 stop on the flash, and I put the flash in rear-curtain sync mode. That gave me the look I was going for. You could still see the colorful stage lighting, but there was enough light to see faces as well.
Obviously, you cant go through all of this while a warbler is flitting around in a tree, but if you know some of this stuff ahead of time, you can at least try to apply it in the field. It might work, or it might not. Chances are it'll mostly work, but you'll have something to try next time, too (like my Flycatcher thread from yesterday). It's a learning process 
