I use 'leave it!' even if it's already in his mouth. 'Leave it' to my dog means stop what you are doing right now, stop forward motion (moving towards object), stop chewing motion, stop chasing motion, stop gulping motion, stop tugging motion, stop everything. The MOMENT that has happend, he gets rewarded.
Hondo Von Dopplet L Bauernhof "Hondo"- GSD
Lilie's Tug McGraw "Tug" - Golden Retriever
Maggie - Mini Dachshund (Rescue)
Lonestar Pivo - Texas Blue Lacy
Ashe - Barn Cat
Katie / APHA