is it normal to have a bit of exhaust smoke coming out of that engine breather at the top of the engine. i noticed it earlier, i though something was cooking fo a minute but its just exhaust smoke, there brilliant compression on all the cyliners. As you may know, the bike had been running significantly rich for a while, but now is back to factory setting, could it be that it may have got coked up or something, and now its running properly, its burning it off? because dont engine run hotter the leaner they are?

Engines do run hotter when they are leaner, but the only the piston and cylinder inner surface areas, as the cooling system takes care of the rest of the engine.

My CBR doesn't smoke from that breather, however other bikes and cars that I have had have done. It is quite normal on some engines, and yours may be one of them plus it was previously a rich black smoke belcher! If the engine is now runnig on the correct mixture and the cooling system is working then I would say there is nothing that needs/could be done to rectify it.

There should not be any smoke out of the breather. If it is the smoke from combustion then you got to think where it has come from...and the only way for the smoke to get into the bottom of the motor is past the rings.

The breather should vent only hot and slightly oly air into the airbox..or into a catch bottle if you don't like the idea of your filter getting minging.