If the next stage (list) in a Kanban is full (at it's Work In Progress (WIP) limit) then it seems you should/can not move the finished card to that List. Only solution I see is to split each list into Doing and Done.
One subtle issue with Kanban is that if you have 3 stages/lists, such as:
...And Design list is "full" (at the Work In Progress limit) then if you finish a Card in Spec, you can't add it to Design (b/c it's full). But if you leave it in Spec, you don't know it's done. (The List it's in communicates it's status).
So it seems that you need to split each List into:
- Spec Doing
- Spec Done
- etc, etc.
Hopefull, the Done doesn't normally have a lot in it.
Or, do you move the card anyway, ignore the WIP limit (for the time being) but then remember that you should not add any more work to the input of this board (which kinda defeats the purpose of the Kanban WIP limits). The won't be communicated "upstream".
FYI, I am using Trello for my Kanban wbboard.