Turns out I was wrong. Fact checked myself and what I was able to do was heal the doed BEFORE knocking it out, which allowed me to achieve peak taming effectiveness after the rex very nearly killed it. That said, I verified I was wrong, you can't improve taming effectiveness by healing the dino with the owl AFTER it's knocked out.

However, what you CAN do, is heal something before it goes down if it's properly trapped which is still very useful. A good application of this would be rock elementals, which are notoriously difficult to knock out without taking too much damage to keep max effectiveness. If properly distracted, you can heal them with the owl before you make those last two or three cannon ball shots.

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