On Marie G, I have modern ropes that remember twist very well, so I sew on a thin line and takes it all on deck, stretch the haliyard all out to take out the twist, and remounts it by use of the thin line. It is also possible to Mount a swivel on the standing end, either mast or yard, (mine is on the yard). My sheet is also sporting a swivel on the standing end to take out the twist. 

Arion has two single blocks shackled at the masthead, with the sheaves flat against the mast as recommended, and a single block on the yard, none of which can swivel.  When I hoist the sail I just let the halyard fall into the cockpit, then later flake it tail first into a plastic box that sits in a corner of the cockpit seat.  (Actually, the halyard has some reserve length and the tail is always in the box.)  I have never had a tangle with this system - it always runs out freely and the halyard never twists.  I am using 10mm double braid line.

I agree with Brian on not using swivel blocks and not coiling the halyard ( I stuff it in a bag, as taught to me by a mountain climber).

In addition it helps to not collect all the parts in one block at each end. This way, used on Johanna's 5-part halyard, works well. (If the link goes on strike, check Arne's sketches under my member's photo album)

Using a multipart purchase only on the fall down from the mast top has one disadvantage, mentioned in PJR: The compression load on the unstayed mast will be higher and that is not desirable.

Arne

Hi Don. Eliminating the swivel and not coiling the tail end of the halyard would help.