We address a difficult, yet under-investigated class of planning problems: fully-observable nondeterministic (FOND) planning problems with strong cyclic solutions. The difficulty of these strong cyclic FOND planning problems stems from the large size of the state space. Hence, to achieve efficient planning, a planner has to cope with the explosion in the size of the state space by planning along the directions that allow the goal to be reached quickly. A major challenge is: how would one know which states and search directions are relevant before the search for a solution has even begun? We first describe an NDP-motivated strong cyclic algorithm that, without addressing the above challenge, can already outperform state-of-the-art FOND planners, and then extend this NDP-motivated planner with a novel heuristic that addresses the challenge.