This paper is about dimensionality reduction by variable selection in high–dimensional real–world control problems, where designing controllers by conventional means is either impractical or results in poor performance. In this paper we propose a novel model–free variable selection approach that, starting from a dataset of one–step state transitions and rewards, identifies which state, control, and disturbance variables are most relevant for control purposes, and reduces the problem dimensionality by removing the others. The core of the procedure is the Recursive Variable Selection (RVS) algorithm, which, starting from the subset of variables needed to explain the reward, recursively repeats the variable–selection procedure on the state variables that have been selected, but whose transition model still needs to be explained. The set of selected variables is incrementally built by adding the best variables provided by a ranking algorithm based on a statistical measure of significance that accounts for non-linear dependencies. The effectiveness of the proposed methodology is tested on two real–world control problems: balancing of a two–wheeled inverted–pendulum robot and the operation of Tono Dam (JP) modeled with a coupled 1D hydrodynamic-ecological model. Preliminary results show that the proposed variable selection approach significantly simplifies the learning of good control policies and can highlight interesting properties of the system to be controlled.