Some players prefer to have no wax at all on their wooden didj mouthpieces. They play the didj "raw," that is with no beeswax added - just lips on wood.
Of course it's not always possible to have a didj with a perfectly sized mouthpiece opening, since this is determined by the tree ! If the opening is too large, then there's no choice but to add wax. In the case when the opening is just right (or slightly smaller), a little bit of smoothing work with a rasp is all that is needed to make a comfortable mouthpiece.
David Hudson uses this method. Most of his didj'es are "raw". Since he makes his own didj's, he can pick and choose what wood he'll take, thus avoiding the size problem. He then shapes the mouthpiece with a rasp so that it fits his mouth perfectly. This way he ensures a perfect fit.
There's a really good reason why David prefers this method. He explains how when you have a wax mouthpiece and a friend wants to play your didj, the first thing that happens is that the mouthpiece gets modified to suit your friend. Once the friend is finished playing and returns the didj, you find that your perfect mouthpiece no longer fits! The Solution ? Make a mouthpiece that you can't modify.
This may sound a bit extreme, since beeswax is pretty hard. Remember though that the Aborigine players use the wonderful, intoxicatingly fragrant wax produced by the Australian "sugarback," a small stingless bee, for their mouthpieces. This wax is almost black in colour, and is much more malleable than regular beeswax at room temperature. The reason why we don't see much of this stuff around is that it is very hard to obtain, and is thus used very sparingly.