Archetypal falling behaviors of impervious objects are classified into four modes: fluttering, tumbling, steady descent, and chaotic motion. The classical scenario predicts these behaviors to be affected by three dimensionless quantities: thickness-to-width ratio, dimensionless inertia, and Reynolds number. In this article we explore experimentally the effect of permeability and porosity on the falling regimes of porous plates. By drilling several hole distributions in rectangular plates, both permeability and porosity are varied systematically. We discover that the introduction of porosity affects the stability of the falling regimes eliminating tumbling. Using a phenomenological model we show that a decrease in circulation induced by the introduction of holes is the primary mechanism for stabilizing the plates' trajectories.