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In most cases a double clicke shoud be checked as if (e.getClickCount() >= 2) - not ' == 2'
That is because it is too dificult to hit button precisely 2 times. Very often we hit 3 and even more.
I've never had this problem, but triple-click usually has a different meaning in a text area : it selects a line instead of a word with a double-click. So we might expect another behavior for a triple-click on a tag, although I'm not sure what...
You probably already know this, but you can change the double or triple click delay in the system preferences if you find it too fast or too slow.
I faced this problem when i used wacom tablet panel. So with it in java double-clickes very often did not work. In a debuger in a new dialog i get single and treaple clicks but not double. Of course you could say that it is problem with drivers. But it ocсures only in Java and in many cases similar problems can be solved just by checkin for many-clicked events. I don't speak about controls which have special behavior for triple-click.