Significance Slow–fast systems arise in many scientific applications, in particular in atmospheric and oceanic flows with fast inertia–gravity waves and slow geostrophic motions. When the slow and fast variables are strongly coupled—symptomatic of breakdown of slow-to-fast scales deterministic parameterizations—it remains a challenge to derive reduced systems able to capture the dynamics. Here, generic ingredients for successful reduction of such systems are identified and illustrated for the paradigmatic atmospheric Lorenz 80 model. The approach relies on a filtering operated through a nonlinear parameterization that separates the full dynamics into its slow motion and fast residual dynamics. The latter is mainly orthogonal to the former and is modeled via networks of stochastic nonlinear oscillators, independent of the slow dynamics.