We investigate simple open few-body systems, the spectra of which exhibit fluctuating patterns, and review the conditions for the existence of an Ericson regime in deterministic, open quantum systems. A widely used criterion, the Lorentzian shape of the autocorrelation function of the spectrum, is shown to be insufficient for the occurrence of Ericson fluctuations: integrable systems or open systems that are not in the Ericson regime might display such an autocorrelation function. We also investigate the sensitivity of Ericson fluctuations on simplified models of realistic systems. In particular, we show that a simplified hydrogenic model for alkali atoms in crossed magnetic and electric fields does not yield Ericson fluctuations for a choice of the energy and field parameters where the realistic system is in the Ericson regime.