  We study several explicit finite index subgroups in the known complex
hyperbolic lattice triangle groups, and show some of them are neat, some of
them have positive first Betti number, some of them have a homomorphisms onto a
non-Abelian free group. For some lattice triangle groups, we determine the
minimal index of a neat subgroup. Finally, we answer a question raised by
Stover and describe an infinite tower of neat ball quotients all with a single
cusp.
