Accurate values for population estimates are always a challenge and can be further burdened in scenarios with high migrant mobility. In these cases, bias emanating from over-coverage, i.e., resident individuals whose death or emigration is not registered, may result in significant ramifications for policymaking and research. In this talk, we will consider different approaches to obtain over-coverage estimates, using Swedish Population registers for the period 2003-2016. We will discuss difficulties regarding the high dimensionality of the data and we will show current developments and ideas for the future.