Active Learning (AL) is a human-in-the-loop framework to interactively and adaptively label data instances, thereby enabling significant gains in model performance compared to random sampling. AL approaches function by selecting the hardest instances to label, often relying on notions of diversity and uncertainty. However, we believe that these current paradigms of AL do not leverage the full potential of human interaction granted by automated label suggestions. Indeed, we show that for many classification tasks and datasets, most people verifying if an automatically suggested label is correct take $3\times$ to $4\times$ less time than they do changing an incorrect suggestion to the correct label (or labeling from scratch without any suggestion). Utilizing this result, we propose CLARIFIER (aCtive LeARnIng From tIEred haRdness), an Interactive Learning framework that admits more effective use of human interaction by leveraging the reduced cost of verification. By targeting the hard (uncertain) instances with existing AL methods, the intermediate instances with a novel label suggestion scheme using submodular mutual information functions on a per-class basis, and the easy (confident) instances with highest-confidence auto-labeling, CLARIFIER can improve over the performance of existing AL approaches on multiple datasets -- particularly on those that have a large number of classes -- by almost 1.5$\times$ to 2$\times$ in terms of relative labeling cost.