Testing concurrent systems requires exploring all possible non-deterministic interleavings that the concurrent execution may have. This is because any of the interleavings may reveal the erroneous behaviour. In testing of actor systems, we can distinguish two sources of non-determinism: (1) actor-selection, the order in which actors are explored and (2) task-selection, the order in which the tasks within each actor are explored. This paper provides new strategies and heuristics for pruning redundant state-exploration when testing actor systems by reducing the amount of unnecessary non-determinism. First, we propose a method and heuristics for actor-selection based on tracking the amount and the type of interactions among actors. Second, we can avoid further redundant interleavings in task-selection by taking into account the access to the shared-memory that the tasks make.