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

Mapnik: http://tile.openstreetmap.org/mapnik/9/341/154.png
Yandex: http://vec.maps.yandex.net/tiles?l=map&v=2.4.1&x=341&y=154&z=9
Yahoo: http://maps1.yimg.com/hx/tl?v=4.2&.intl=en&r=1&x=341&y=101&z=10
Bing: http://ecn.t2.tiles.virtualearth.net/tiles/r121032121.png?g=383&mkt=en-us&shading=hill

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?