We present two novel extensions of an on-line importance weighted active learning algorithm IWAL, using the properties of disagreement values among hypotheses. The first extension, DIWAL, prunes the hypothesis set with a more aggressive strategy based on concentration bounds with disagreement values. We show that DIWAL improves the generalization performance and the label complexity of the original IWAL, and further quantify the improvement in terms of the disagreement graph coefficient. The second extension, ZOOM, adaptively zooms into the function space near the best-in-class hypothesis, which effectively reduces the best-in-class error and thus simultaneously improves the generalization performance and the label complexity. We report experimental results on multiple datasets and demonstrate that the proposed algorithms achieve better test performances than IWAL given the same amount of labeling budget.