The most efficient way, of course, to slim down the line would be, as Somebody suggested, to limit the number of eligible persons by proximity of blood to the last monarch. In the Netherlands, they use a cutoff in the third degree of consanguinity, which would include children, grandchildren, great-grandchildren, siblings, nephews/nieces, and uncles/aunts of the monarch, but no cousins. The UK could go one degree further, i.e. up to the fourth degree, to include first cousins as well.
Again, the reason why, I think, that is not done is that it is considered innocuous anyway to have an unbounded line of succession as long as the Royal House properly is limited.