Traditional analytical reflectance models, while compact and interpretable, lack the capacity to accurately represent physical measurements. Recent neural models, which closely fit input data, are less generalizable and often more expensive to store and evaluate. To combine the strengths and overcome the limitations of these two classes of models, we present neural enhancement, a novel framework to boost an input analytical appearance model, by identifying and replacing its key computational nodes/operators with small-scale multi-layer perceptrons. This allows us to leverage the computational graph structure of the original model, while improving its expressiveness at a modest cost. To make the enhancement computationally tractable, we propose a hypercube-based search to automatically and efficiently identify the node(s) and/or operator(s) to be replaced towards maximal gain in a differentiable fashion. We enhance a number of common analytical BRDF models. The results are, at once accurate, compact and efficient, and compare favorably with state-of-the-art work on fitting measured reflectance. Finally, our models are fully compatible with standard rasterization or ray-tracing pipeline.