Gabor kernels are widely accepted as dominant filters for iris recognition. In this work we investigate, given the current interest in neural networks, if Gabor kernels are the only family of functions performing best in iris recognition, or if better filters can be learned directly from iris data. We use (on purpose) a single-layer convolutional neural network as it mimics an iris code-based algorithm. We learn two sets of data-driven kernels; one starting from randomly initialized weights and the other from open-source set of Gabor kernels. Through experimentation, we show that the network does not converge on Gabor kernels, instead converging on a mix of edge detectors, blob detectors and simple waves. In our experiments carried out with three subject-disjoint datasets we found that the performance of these learned kernels is comparable to the open-source Gabor kernels. These lead us to two conclusions: (a) a family of functions offering optimal performance in iris recognition is wider than Gabor kernels, and (b) we probably hit the maximum performance for an iris coding algorithm that uses a single convolutional layer, yet with multiple filters. Released with this work is a framework to learn data-driven kernels that can be easily transplanted into open-source iris recognition software (for instance, OSIRIS -- Open Source IRIS).