Recently, Lobato (Journal of the American Statistical Association, 96, 1066-76, 2001) proposed a robust test of no autocorrelation on a time series when the series is possibly dependent. While the Lobato test is shown to be accurate in size, its power performance is unsatisfactory. This paper seeks to improve the power of the Lobato test without comprising its good size property. Based on the recent works of Jansson (2004) and Phillips et al. (2003), two classes of modified Lobato tests are suggested. It is found that the Lobato test and its Phillips-Sun-Jin modification exhibit very similar control over size while the Jansson modification tends to be more vulnerable to size distortion. It is also found that both modified tests dominate the Lobato test in terms of local asymptotic power and in terms of finite sample power and the Phillips-Sun-Jin modification seems to outperform the Jansson modification. Autocorrelations in monthly financial asset (stock/bond) returns are investigated.