In reply to MikeTS:
The key is to acclimatise properly without artificial aids. Walk in starting from around 1000 metres, and very slowly ascending only 1000 metres each day, and I mean slowly, even if its only a couple of miles, take all day and drink plenty.
On the third day you will be at 4000 metres fully acclimatised, but don't go higher on the fourth day.
This was the advice of a guide I hired, who kept having to stop me walking/climbing too fast, insisting frequent sit downs for deep meaningful conversations and a drink. We then slept each night at around 4,500 metres, and climbed to over 5000 metres each day, and I never had the slightest problem.
His advice was "Don't hit altitude, or it will hit you back. You have to sneak up on it so it doesn't notice."