RE: another BT-32EI question/problem
OK, missed the comment on the carb screen.
One thing to check would be the crankcase or cylinder screws. We've seen a few crankcases cracked just below the cylinder, and we've also seen loose screws that retain the cylinder to the case. This causes air leaks into the lower-end, which leans the mixture. You notice this at higher settings because the added RPM tends to cause more pressure leakage. Sometimes, if the case is cracked, it's hidden by the engine mounting plate.
If the engine still looks OK, send it to us for checking out.