General Points about Heuristics

Unfortunately, A* often suffers because it cannot venture down a single path unless it is almost continuously having success (i.e., h is decreasing). Any failure to decrease h will almost immediately cause the search to switch to another path.
In order to devise an admissible heuristic, h must frequently be very simple and therefore resorts to (almost) uniform-cost search through parts of the search space.
If optimality is not required, using a heuristic that occasionally overestimates the actual cost but is usually very close to the actual cost (over or under), will result in many fewer nodes being expanded to find a solution than using a provably admissible heuristic.