The existence of feebly interacting massive particles (FIMPs) could have significant implications on the effective number of relativistic species N-eff in the early Universe. In this work, we investigate in detail how short-lived FIMPs that can decay into neutrinos affect N-eff and highlight the relevant effects that govern its evolution. We show that even if unstable FIMPs inject most of their energy into neutrinos, they may still decrease N-eff, and identify neutrino spectral distortions as the driving power behind this effect. As a case study, we consider heavy neutral leptons (HNLs) and indicate which regions of their parameter space increase or decrease Neff. Moreover, we derive bounds on the HNL lifetime from the cosmic microwave background and comment on the possible role that HNLs could play in alleviating the Hubble tension.