The method is carried out for continuously producing a liquefied methane gas (LMG) from a pressurized mixed methane gas feed stream. It is particularly well adapted for use in relatively small LMG distributed production plant, for instance those ranging from 400 to 15,000 MT per year, and/or when the mixed methane gas feed stream has a wide range of nitrogen-content proportions, including nitrogen being substantially absent. The proposed concept can also be very useful in the design of medium-scale and/or large-size plants, including ones where the nitrogen content always remains above a certain threshold. The methods and arrangements proposed herein can mitigate losses of methane gas when venting nitrogen, for instance in the atmosphere.