Yeah, I tie the braid straight to the swivel, however the braid has been doubled with either a bimini or a spider hitch. I've heard not to trust spider hitches, but they are so easy/quick to tie I can't not use them. I haven't had one fail me yet (maybe a 1.2m kingy will fully test it one day).
I use only about 6 wraps in the uni if the braid has been doubled, seems not to need the extra wraps when doubled. I also re-tie all my main line doubles and uni's every other trip.
Kingy