Beekeeper,
What a lovely aeroplane you have use of, I have the hope to see it in person some time.
Speaking from Tiger Moth experience, if you're getting two landings for the price of one when attempting a three-pointer, I suspect you're touching down mainwheels slightly first, i.e. in slightly too flat an attitude. The CG being behind the mainwheels, the descending aeroplane has its nose pushed up by the mainwheel contact, increases its angle of attack and flies off again briefly. If you hold off just a little bit longer she will settle down on all three points at once, and if you are nice and low in the hold-off the contact will be satisfylingly gentle, too. You don't say what taildraggers you've been flying hitherto - but the Tiger does have a very high deck angle, the nose is a lot higher in the three-point attitude than in, say, a Cub.
Having said that I don't have a great deal of time on the Tiger and sometimes if I have lots of room, e.g. at Sywell, I'll wheel it on gently at a lowish speed.
Steve - Loads of room under the rotating prop on a Cub, Moth or Chippie. A Griffon Spitfire, Su-26 or a Pitts is another matter, and with them you really do have to keep the prop clearance in mind. (Someone, please check me out on your Griffon Spit and I'll remember the prop, honest I will!) Next time you see a Cub or Moth, stand alongside at a fair distance and hold up a straight edge to sight between the bottom of the prop arc and the main wheels. That will show you just how high the tail has to be for a prop strike on those types - it's really high.