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There are a couple of options. The first is to place the Country field on the filters shelf and select the Top tab. Then, the top N can be inserted.
Another option, that allows for users to interact is to create an integer parameter (you can select the range if desired or create a list if desired). Then, create a calculation similar to the following:
index()<=[Top N parameter]
Then, place this on the filter shelf and select True. Finally, right click on the parameter and select Show Parameter Control.
Hope this helps!
My list is shorter now, but it seems to vary in length arbitrarily when I change the year.
It is an order of operations situation,
The easy answer is you can turn your Year filter into a Context filter, to force the filter on Year to happen before the Top N filter.
The more complex is to use a filter on a calculated field that uses the INDEX() function, and because it is a filter on a table calculation, it will be evaluated after normal filters.
see http://community.tableau.com/message/139603#139603 for more details