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In a recently introduced model of successive committee elections, for a given set of ordinal or approval preferences one aims to find a sequence of a given length of “best” same-size committees such that each candidate is a member of a limited number of consecutive committees. However, the practical usability of this model remains limited, as the described task turns out to be NP-hard for most selection criteria already for seeking committees of size three. Non-trivial or somewhat efficient algorithms for these cases are lacking too. Motivated by a desire to unlock the full potential of the described temporal model of committee elections, we devise (parameterized) algorithms that effectively solve the mentioned hard cases in realistic scenarios of a moderate number of candidates or of a limited time horizon.