On the rec skating newsgroup Bill Schneider has been posting on the FI brackets. I was trying them the other day right before my lesson so coach catches me and we worked on them and my pitiful BI3's. Low and behold if I can force myself to keep my head up and do them almost flat the FI bracket is actually easier and certainly more gentle than the FI3 turn! So here is the penultimate (LOL OK the last thing in the lesson) exercise for my BI3's:

Glide along blue line on a flat on RFI edge (sic) facing to the right with free foot touching at ankle and do a gentle RFI bracket. THen, while keeping the gaze straight to the side step down feet together on a flat LBI edge. Now try the LBI3 - if needed you can push off on R toepick and try to work so free leg stays touching at ankles. For those moments when it clicks try cross front or cross behind before the turn.
Lyle