I suffer from cross-over when shooting targets from left to right, but not right to left.
Like dogon, I learned to shoot everything with one eye closed. I found that I can compensate for the loss of depth perception by starting off with low gun, both eyes open to see the target and gauge the depth. On mounting the gun, I close my right eye.
The best techinque is the one that works best for you, whatever that may be. You just have to be willing to put up with a lot of misses to find it.
Oh, yeah, take her to dinner too!
