In this paper, a new family of shape descriptors called Free Shape Contexts (FSC) is introduced to generalize the existing 3D Shape Contexts. The FSC introduces more degrees of freedom than its predecessor by allowing the level of complexity to vary between its parts. Also, each part of the FSC has an associated activity state which controls whether the part can contribute a feature value. We describe a method of evolving the FSC parameters for the purpose of creating highly discriminative features suitable for detecting specific objects in sparse point clouds. The evolutionary process is built on a genetic algorithm (GA) which optimizes the parameters with respect to cross-validated overall classification accuracy. The GA manipulates both the structure of the FSC and the activity flags, allowing it to perform an implicit feature selection alongside the structure optimization by turning off segments which do not augment the discriminative capabilities. We apply the proposed descriptor to the problem of detecting single standing dead tree trunks from ALS point clouds. The experiment, carried out on a set of 285 objects, reveals that an FSC optimized through a GA with manually tuned recombination parameters is able to attain a classification accuracy of 84.2%, yielding an increase of 4.2 pp compared to features derived from eigenvalues of the 3D covariance matrix. Also, we address the issue of automatically tuning the GA recombination metaparameters. For this purpose, a fuzzy logic controller (FLC) which dynamically adjusts the magnitude of the recombination effects is co-evolved with the FSC parameters in a two-tier evolution scheme. We find that it is possible to obtain an FLC which retains the classification accuracy of the manually tuned variant, thereby limiting the need for guessing the appropriate meta-parameter values.