The National Registry of Emergency Medical Technicians is now advocating immediate use of tourniquets if initial direct pressure is ineffective.
nremt.org/Content/NREMT_Home.nremt (Free Login required)
This is a typically sneaky NREMT trick, as no press release seems to have been made on this station to training institutions; I had to inform my program director. We were training on the old criteria after the new criteria were (quietly) posted on the NREMT website in the section only accessible to registered users.
On the other hand, now we don't have to screw around with pressure points when we know it's going to need surgical repair and can just load-n-go.