My horse also has a weak side. What I would recommend is flexing your horse. Start on the ground and get it to where you can pull your horses head to the girth area with light pressure. Make sure you work both sides equallly.
Next using probably an o-ring or a d-ring, flex you horse, on the ground still, with the bit. After your horse gets the hang of that, get on and try again. Make sure before you release the pressure that your horse is standing still and gives to the pressure.
Next go at a walk and occasionally flex or bend a circle. Remeber work both sides equally. Once your horse gets that: add more speed.
This was featureed in one of Clinton Anderson's dvd's, and it has helped my horse with her leads, because if they have to flex that way, that lead gets easier, so they will become more comfortable with it.
Another thing would be to just lope circles on that lead, slowly adding speed. Letting your horse strengthen that side of the body.
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