We analyse the adaptive limiter control (ALC) method, which was recently proposed for stabilizing population oscillations and experimentally tested in laboratory populations and metapopulations of Drosophila melanogaster. We thoroughly explain the mechanisms that allow ALC to reduce the magnitude of population fluctuations under certain conditions. In general, ALC is a control strategy with a number of useful properties (e.g. being globally asymptotically stable), but there may be some caveats. The control can be ineffective or even counterproductive at small intensities, and the interventions can be extremely costly at very large intensities. Based on our analytical results, we describe recipes how to choose the control intensity, depending on the range of population sizes we wish to target. In our analysis, we highlight the possible importance of initial transients and classify them into different categories.