I'm also sure I'm not the first person to come up with this solution, but just in case you haven't found it yet, here's my tip.
Do you know when you have beautiful briolette that is perfect for the particular piece you're working on, but you want to use heavier gauge wire and the holes in the briolette are just too small? And you don't have a bead reamer, or you do (like me), but it's still not working very well for you?
Well, this is what you do:
Insert the fine gauge wire that fits into the briolette and prepare for wrapping the loop as usual.
Lay a piece of the heavier gauge wire alongside the finer wire (it's a little off center in the picture so you can see clearly).
Bend both wires simultaneously to start the wrapped loop.
Form the loop using the two wires and connect to the other piece you want to attach it to.
Wrap around a few times so that the finer gauge wire is totally secure and then cut it.
Continue wrapping the briolette with the heavier gauge wire until you're happy with the look and cut the remaining wire. Et voila!
Another view of the finished piece.
And if you spotted that on pic 4 I actually attached the briolette to a differente piece than the finished necklace, congratulations! You win a lifelong subscription to the "Spot the Obvious" magazine... :)
I had finished my necklace when I realized maybe someone could use this tip, so redid the whole thing.