Sensory neural circuits rely on a common set of motifs to process inputs, including convergence of multiple inputs to a single neuron, divergence of inputs into parallel pathways, and nonlinearities that are selective for some inputs over others. Past work has detailed how optimized response nonlinearities and synaptic weights can maximize encoded information, but these solutions depend on tightly tuned response functions and connectivities. Our study found that incorporating generic, non-invertible, selectivity-inducing nonlinearities into a circuit with divergent and convergent structure can enhance encoded information despite the information loss induced by the convergence of inputs and the nonlinearities when considered separately. This study extends a broad literature on efficient coding in single neurons to more complex circuits. Our study shows how neural circuits may combine selectivity at the single neuron level with convergent and divergent circuit architectures to flexibly maximize encoded information.