The 3 Couple repeat in 3 couple set can simply be called a 3 Couple set since there is little risk of ambiguity with any other Longwise set format.
The Full set requires three Couples and the dance usually consists of three Repeats, each involving all three Couples. At the end of the first Repeat, the more common Progression leaves the 1st Couple in 3rd place with the 2nd couple in 1st place; the alternative Progression with the 3rd couple Finishing in 1st place and the 1st couple in 2nd place is also possible. This standard form of the dance continues with the 2nd and 3rd couples becoming the 1st couple of the Active set and dancing one Repeat each, in turn; it Finishes with all the dancers in their Original Places.
In this format, unlike the 3 Couple repeat in 4 couple set format, the 1st couple of the Active set have no rest after their performance and so must be ready immediately to perform as a Supporting couple in the next Repeat. Equally, at the end of the first and second Repeats, the Couple now in 1st place must be ready to perform immediately as the 1st couple of the new Active set.
In at least one dance, The Earl of Erroll's Reel, there is no simple Repeat structure; the whole dance is treated as a single entity Finishing with all the dancers in their Original Places though there are some repetitive sequences embedded within it.
The répertoire of Reels and Jigs in this 3 Couple repeat in 3 couple set format is quite limited, as is depressingly obvious to anyone who has attempted to prepare a Scottish Dancing demonstration programme using only three Couples, whether for reasons of space or numbers available. However, the 3 Couple repeat in 4 couple set format contains many familiar dances which can be adapted to the 3 Couple repeat in 3 couple set format by changing the Progression to 231 rather than 213. Similarly, some Ceilidh dances with the 4 Couple repeat in 4 couple set format can easily be adapted for three Couples.
For example, here are some Scottish Country Dances which either have the format, 3 Couple repeat in a 3 couple set, or have been adapted to this format as indicated in the Maxicrib Dance instructions -
The Byron Strathspey
The Cooper's Wife (3-couple version)
The Cumberland Jig (3-couple version)
The Fairbridge Reel
The Gypsy Shawl (3-couple version)
Jennifer's Jig (3-couple version)
The Laird of Milton's Daughter (3-couple version)
Mairi's Wedding (3-couple version)
Macdonald of the Isles
The Montgomeries' Rant (3-couple version)
My Heather Hills
The Sound of Harris
St George's Cross
Virginia Reel (3-couple version)