Everyone loves a waxy new potato. Certainly me and the bread knife do. Here's a way I've found that ensures that they're just how we like them. I commend it to the house.

Scrape the potatoes, set them to boil in salted water (with the lid on please: it halves the amount of gas / electricity needed to keep them boiling). Once they're up to a gentle boil, keep a close eye on their timing. After fifteen minutes, give one or two a prod with a sharp knife to see if they yield in the middle. As soon as they do, turn off the heat and drain, then add a good knob of butter, give them a quick swirl around and the leave them to stand for another fifteen minutes with the lid still on. It's this standing about bit that's the most important part. It helps the waxiness to "set", or least in some way become maximally waxy, and for the butter to soak in making them doubly scrummy.

But you know, I'm never sure about mint. I usually leave it out.

Now, does anyone have Heston Blumenthal's telephone number?

Thanks FelisLeiter for this tip - I had always put waxiness down to variety and nothing else. But, having read your post I now realise that you are absolutely right about the period left standing making a difference.
I boiled some international kidney potatoes to eat straight away and they were really disappointing. The next batch I cooked for salad which meant leaving them in the saucepan to cool (drained of course and lid on). The results were completely different - not waxy but the texture and the taste were so different I was suspecting I'd actually cooked a different variety.
(The salad was delicious, potatoes served in mayonnaise with a good sprinkling of freshly chopped mint and ground rock salt. Mmmmm).

If you're feeling reckless, a dribble of Truffle Oil instead of butter goes down pretty well as well

But first, grow some truffles...

Or rich.

Where we lived in Ayrshire was about a five minute walk from the fields where the Ayrshire Potatoes were grown, you know the ones where the farmer spread seaweed from the beach every winter. When the potatoes were picked (by hand) we were allowed into the fields to gather the small ones left. We would take a bag home and these were immediately put on to boil.

When they were ready they were coated in butter and then sprinkled with pinhead oatmeal and chopped chives. - delicious