A simple point of an object is a point whose removal does not change the topology. However, the simultaneous deletion of simple points may change the topology. A popular way for overcoming this problem is to use a directional strategy. This method has good properties in 2D discrete spaces but it does not work in 3D. Through the notion of P-simple point we propose a general strategy for removing points in parallel without altering the topology of a 3D space. We derive some new sufficient conditions such that any parallel thinning algorithm satisfying these conditions is ensured to preserve topology.