  We study combinatorial games under mis\`ere convention. Several sets of games
have been considered earlier to better understand the behaviour of mis\`ere
games. We here connect several of these sets. In particular, we prove that
comparison modulo binary dicot games is often the same as comparison modulo
dicot games, and that equivalence modulo dicot games and modulo impartial games
are the same when they are restricted to impartial games.
