Abstraction is a common method to compute lower bounds in classical planning, imposing an equivalence relation on the state space and deriving the lower bound from the quotient system. It is a trivial and well-known fact that refined abstractions can only improve the lower bound. Thus, when we embarked on applying the same technique in the probabilistic setting, our firm belief was to find the same behavior there. We were wrong. Indeed, there are cases where every direct refinement step (splitting one equivalence class into two) yields strictly worse bounds. We give a comprehensive account of the issues involved, for two wide-spread methods to define and use abstract MDPs.