  For the baby Skyrme model with a specific potential, compacton solutions,
i.e., configurations with a compact support and parabolic approach to the
vacuum, are derived. Specifically, in the non-topological sector, we find
spinning Q-balls and Q-shells, as well as peakons. Moreover, we obtain compact
baby skyrmions with non-trivial topological charge. All these solutions may
form stable multi-soliton configurations provided they are sufficiently
separated.
