The concept of periocular biometrics emerged to improve the robustness of iris recognition to degraded data. Being a relatively recent topic, most of the periocular recognition algorithms work in a holistic way and apply a feature encoding/matching strategy without considering each biological component in the periocular area. This not only augments the correlation between the components in the resulting biometric signature, but also increases the sensitivity to particular data covariates. The main novelty in this paper is to propose a periocular recognition ensemble made of two disparate components: 1) one expert analyses the iris texture and exhaustively exploits the multispectral information in visible-light data and 2) another expert parameterizes the shape of eyelids and defines a surrounding dimensionless region-of-interest, from where statistics of the eyelids, eyelashes, and skin wrinkles/furrows are encoded. Both experts work on disjoint regions of the periocular area and meet three important properties. First, they produce practically independent responses, which is behind the better performance of the ensemble when compared to the best individual recognizer. Second, they do not share particularly sensitivity to any image covariate, which accounts for augmenting the robustness against degraded data. Finally, it should be stressed that we disregard information in the periocular region that can be easily forged (e.g., shape of eyebrows), which constitutes an active anticounterfeit measure. An empirical evaluation was conducted on two public data sets (FRGC and UBIRIS.v2), and points for consistent improvements in performance of the proposed ensemble over the state-of-the-art periocular recognition algorithms.