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Multiobjectivization, the optimization of a single-objective problem by adding objectives, has recently received interest by researchers. Studying multiobjectivization on an abstract problem can assist in understanding the fundamental drivers of the improvements in performance that multiobjectivization achieves in some situations. Previously created abstract problems do not appear to provide the modeling power needed to study the benefits of this new family of optimization techniques. The tunable objectives problem (TOP) model is introduced to help demonstrate how problem features such as objective-convolution, multiple layer epistasis, the presence of local optima, and layered problem structure are related to the performance of multiobjectivization via helper objectives. Experiments using TOP demonstrate how multiobjectivization via helpers improves the signal-to-noise in a genetic algorithm and identifies several general problem difficulties that, when present, are likely to increase the need for multiobjectivization.