If I had not been to KTP, I would have gone immediately after reading your description.

In KNP, the crowds have never been a problem for me, maybe because I always go in the summer when the school holidays have finished. I have had days without meeting more than a few cars far apart, lion sightings all to myself, waterhole watching with no other vehicle in sight, etc.
Squirrels
Marvellous "exhibition" of the bee-eaters in very special attitudes

and the secretary birds "out to dry" nonetheless!
Giraffes in knots
