According to the resemblance nominalism, properties depend on primitive resemblance relations among particulars, while there are neither universals nor tropes. Rodriguez-Pereyra (Resemblance nominalism. A solution to the problem of universals, 2002) contains a systematic formulation and defence of a version of resemblance nominalism according to which properties exist, conceived of as maximal classes of exactly precisely resembling particulars. In this chapter, I raise a couple of objections against Rodriguez-Pereyra's version of resemblance nominalism. First, I argue that Rodriguez-Pereyra's solution to the so-called imperfect community difficulty is untenable. Second, I argue that Rodriguez-Pereyra's idea that sparse properties are bound to be lowest determinates, while determinable properties of any degree are to be treated as (infinite) disjunctions of determinates, is liable to undermine the whole approach.