In the first part of this survey, we review how the power of two choices underlies space-efficient data structures like cuckoo hash tables. We’ll find that the additional power afforded by more than 2 choices is often outweighed by the additional costs they bring. In the second part, we present a data structure where choices play a role at coarser than per-element granularity. In some sense, we rely on the power of (1+\epsilon) choices.