With the discovery of a particle that seems rather consistent with the minimal Standard Model Higgs boson, attention turns to questions of naturalness, fine-tuning, and what they imply for physics beyond the Standard Model and its discovery prospects at run II of the LHC. In this article we revisit the issue of naturalness, discussing some implicit assumptions that underly some of the most common statements, which tend to assign physical significance to certain regularization procedures. Vague arguments concerning fine-tuning can lead to conclusions that are too strong and perhaps not as generic as one would hope. Instead, we explore a more pragmatic definition of the hierarchy problem that does not rely on peeking beyond the murky boundaries of quantum field theory: we investigate the fine-tuning of the electroweak scale associated with thresholds from heavy particles, which is both calculable and dependent on the nature of the would-be ultraviolet completion of the Standard Model. We discuss different manifestations of new high-energy scales that are favored by experimental hints for new physics with an eye toward making use of fine-tuning in order to determine natural regions of the new physics parameter spaces. © 2014 American Physical Society.