My hors takes off a stride early on small jumps and ALWAYS overjumps. How can I help him to calmly jump small jumps without jumping them like they're 50cm higher than they are.

For the leaving out a stride: You have to be clear and decide where he puts his feet. He's obviously becoming too excited and rushing past your hand to the fence. Try half halting a few extra times on your way in, and add a stride on your way into the fence. This extra stride can be several strides away, but it'll still get him waiting. If he doesn't allow for this extra stride, then half before the jump to make it clear that you decide when he does and doesn't jump.
In terms of the overjunping, at least he's being cautious. To get him to stop overjunping, you can put him on a circle with a small jump on it, trotting in. Simply take him in a circle over and over again until he becomes bored of the jump, and realizes that there's nothing special about it . This will also help with the leaving out a stride.
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