We propose an efficient method for reproducing diffraction colours on natural surfaces with complex nanostructures that can be represented as height-fields. Our method employs Chebyshev approximations to accurately model view-dependent iridescences for such a surface into its spectral bidirectional reflectance distribution function (BRDF). As main contribution, our method significantly reduces the runtime memory footprint from precomputed lookup tables without compromising photorealism. Our accuracy is comparable with current state-of-the-art methods and better at equal memory usage. Furthermore, a Chebyshev polynomial basis set with its near-best approximation properties allow for scalable memory-vs-performance trade-offs. We show realistic diffraction effects with just two lookup textures for natural, quasi-periodic surface nanostructures. Performance intensive applications like games and VR can benefit from our method, especially for low-end GPU or mobile platforms.