Compared to one-parameter persistence modules, multiparameter modules are richer, more flexible and have better stability properties. On the other hand, multiparameter modules do not always decompose nicely into interval modules like one-parameter modules do, and this is arguably the main disadvantage of multiparameter persistence. This is not just a theoretical worst-case statement; also modules arising from data tend to have complicated indecomposable components. In earlier work, I introduced prunings, which is an invariant that breaks almost-decomposable modules apart into approximate components. I will talk about ongoing work with Jan Jendrysiak and Fabian Lenzen about computing prunings in practice. One goal is to produce decompositions with the same advantages as the one-parameter barcodes/persistence diagrams: a simplified summary with one component per feature of the data set (instead of one big mysterious blob). Another is to shed light on the structure of multiparameter modules arising from data, which is still poorly understood.