We consider the problem of efficiently exploring the arms of a stochastic bandit to identify the best subset of a specified size. Under the PAC and the fixed-budget formulations, we derive improved bounds by using KL-divergence-based confidence intervals. Whereas the application of a similar idea in the regret setting has yielded bounds in terms of the KL-divergence between the arms, our bounds in the pure-exploration setting involve the ``Chernoff information'' between the arms. In addition to introducing this novel quantity to the bandits literature, we contribute a comparison between strategies based on uniform and adaptive sampling for pure-exploration problems, finding evidence in favor of the latter.