Recently, Mission Hills Croquet Pro Ben Rothman ran a tournament using Rugby Blocks, and the format worked wonderfully.
In Rugby Blocks, instead of playing all the other players in the same block, each player in one block plays all the players in another block. This has several advantages over the usual Round-Robin Blocks.
1. Each player in a Rugby Block plays one more game than in a Round-Robin Block.
2. Each player in a Rugby Block plays exactly the same opponents as all the other players in that block. So the block results that are used for seeding a subsequent knockout are more accurate.
For example, consider two blocks (A and B) with four players each (A1, A2, ..., B1, B2, ...). In Round-Robin Blocks player A1 would play A2, A3, and A4, but player A2 would play A1, A3, and A4.
If player A1 was Ben Rothman, you can see that he has an easier schedule than player A2 -- he doesn't play the #1 player in North America. In Rugby Blocks players A1 and A2 both play B1, B2, B3, and B4.
3. Players in each of the Rugby Blocks are kept together in the subsequent knockout. This means that they don't play someone they met in the Rugby Blocks until the final!
In the two four-player blocks example above, assuming that the players finished the Rugby Blocks in numerical order, the knockout would be seeded as follows.
I wish this format were used more often.