Best kept secret in ARK:

Bring the Snow Owl for KO tames. Normally, if the dino got low on health before it went down, you'll lose a lot of taming effectiveness. However, if you use the owl's healing ability to bring the sleeping dinos HP back up *before* you start feeding it, you will not lose any taming effectiveness because of damage. Furthermore, if crap happens and something hurts the dino and drops the TE after you've already started, you can heal them, let them wake up, and start over if you're determined to tame it with max bonus levels.

Note: I tested this with a Doedicurus that was down to a silver of HP because a rex decided to attack just as I was knocking it out. I retained 100% taming effectiveness by fully healing it with the owl before feeding it any kibble to tame it. Takes a lot of the stress out of any KO tame since the heal works on all dinos, tame or wild, and even the riding survivor.