Explicit classical-limit formulae for two leading spectral moments characterizing the anisotropy of the interaction potential are derived for fast collisions of linear rotators in the binary regime. With the help of these moments, model Fourier-transforms of the time-correlation functions comprising non-Markovian effects are restored, which enables a novel and straight approach to pressure transformation of broad spectral bands and pressure-broadening characteristics of (vib)rotational spectral lines, as demonstrated on a simple Markov-limit example of isotropic and anisotropic Raman line widths of molecular nitrogen.