One of key topics in fMRI analysis is discovery of task-related brain areas. We focus on predictive accuracy as a better relevance measure than traditional univariate voxel activations that miss important multivariate voxel interactions. We use sparse regression (more specifically, the Elastic Net 1) to learn predictive models simultaneously with selection of predictive voxel subsets, and to explore transition from task-relevant to task-irrelevant areas. Exploring the space of sparse solutions reveals a much wider spread of task-relevant information in the brain than it is typically suggested by univariate correlations. This happens for several tasks we considered, and is most noticeable in case of complex tasks such as pain rating; however, for certain simpler tasks, a clear separation between a small subset of relevant voxels and the rest of the brain is observed even with multivariate approach to measuring relevance.