This paper explores avenues to improve VaR backtesting against violations of unconditional coverage, with emphasis on detecting underestimates of risk. I show that existing tests for unconditional coverage have an undesirable asymmetry in power, making them less (more) effective at detecting underestimates (overestimates) of risk. A set of Lagrange multiplier (LM) tests is proposed, leading to improved power against the more dangerous underestimates. Also, the use of one-sided coverage tests is revisited, with a one-sided version of the new LM test performing best. Results are supported by simulations, showing the effectiveness of the new tests in finite samples. The same issues of asymmetric power are shown to carry over to the case of conditional coverage, though it appears that finite sample issues affecting the independence component of the tests can adversely impact performance. A simple weighted test statistic is shown to help alleviate this problem, providing an avenue to exploit the advantages of the LM approach in a conditional coverage setting.