Yandex' tiles shifted north

Following tiles have the same tilenumber: level=9(for yahoo 10), x=341, y=154. You see mapnik, yandex, yahoo and bing.
Yandex tiles lay a little bit more to the north. The deviation depends on the zoomlevel.

Mapnik Yandex Yahoo Bing


For my program that can display different maps (also next to each other), because of this north shift, I have to adapt the code for converting lat,lon to tilenumbers and back. I need to know the relation between north shift and zoomlevel. Who tackled this before or has some info?