We propose a procedure for the locally optimal window width in nonparametric spectral estimation, minimizing the asymptotic mean square error at a fixed frequency of a lag-window estimator. Our approach is based on an iterative plug-in scheme. Besides the estimation of a spectral density at a fixed frequency, e.g. at frequency zero, our procedure allows to perform nonparametric spectral estimation with variable window width which adapts to the smoothness of the true underlying density.