Parameter servers (PSs) facilitate the implementation of distributed training for large machine learning tasks. A key challenge for PS performance is that parameter access is non-uniform in many real-world machine learning tasks, i.e., different parameters exhibit drastically different access patterns. We identify skew and nondeterminism as two major sources for non-uniformity. Existing PSs are ill-suited for managing such non-uniform access because they uniformly apply the same parameter management technique to all parameters. As consequence, the performance of existing PSs is negatively affected and may even fall behind that of single node baselines. In this paper, we explore how PSs can manage non-uniform access efficiently. We find that it is key for PSs to support multiple management techniques and to leverage a well-suited management technique for each parameter. We present Lapse2, a PS that replicates hot spot parameters, relocates less frequently accessed parameters, and employs specialized techniques to manage nondeterminism that arises from random sampling. In our experimental study, Lapse2 outperformed existing, single-technique PSs by up to one order of magnitude and provided near-linear scalability across multiple machine learning tasks.