When a water drop hits a superhydrophobic solid surface, it bounces off the substrate like an elastic ball. Here we show that when a tiny superhydophobic solid sphere impacts with water, it can bounce off the free surface just as it impacts with an elastic membrane. The motion of a sinking sphere is analytically calculated by solving a potential flow whose free boundary is determined by the Young-Laplace equation. To find conditions under which the solid sphere should sink, bounce off, or oscillate upon impact with water, we construct simple scaling laws which are shown to agree well with experimentally found boundaries between the distinct impact behaviors in a regime map based on dimensionless parameters.