Current techniques for security analysis of administrative role-based access control (ARBAC) policies restrict themselves to the separate administration assumption that essentially separates administrative roles from regular ones. The naive algorithm of tracking all users is all that is known for the analysis of ARBAC policies without separate administration, and the state space explosion that this results in precludes building effective tools. In contrast, the separate administration assumption greatly simplifies the analysis since it makes it sufficient to track only one user at a time. However, separation limits the expressiveness of the models and restricts modeling distributed administrative control. We undertake a fundamental study of analysis of ARBAC policies without the separate administration restriction, and show that analysis algorithms can be built that track only a bounded number of users, where the bound depends only on the number of administrative roles in the system. Using this fundamental insight paves the way for us to design an involved heuristic to further tame the state space explosion in practical systems. Our results are also very effective when applied on policies designed under the separate administration restriction. We implement our techniques and report on experiments conducted on several realistic case studies.