The compy's torpor drains faster than almost any other creature in the game. Put narcotics into it's inventory before you even put the meat in. If you don't have narcotics, you won't even have time to run to the nearest buddy and pick narcoberries before it wakes up.
I found a level 1(by chance), and it took me 14 seconds to tame. I found thirteen more over the month, and by February(found my first one at January), I had an army. I took down a whole Allosuarus in seconds with the army, but we had a PVP war, and..........eleven fell to my enemy's Trexes and Baryonyx. Only one remains now, and I keep him in my ark Basement. His names JasonBourne