Optical fibers with sub-wavelength cores are promising systems for efficient nonlinear light generation. Here we reveal that the single-mode criterion represents a convenient design tool to optimize the performance of nonlinear fibers circumventing intense numerical calculations. We introduce a quasi-analytic expression for the nonlinear coefficient allowing us to investigate its behavior over a large parameter range. The study is independent of the actual value of the material nonlinearity and shows the fundamental dependencies of the nonlinear coefficient on wavelength, refractive index and core diameter, elucidated by detailed case studies of fused silica and chalcogenide tapers and hybrid fibers.