It is proved that the variable sampling interval (VSI) type charts are a useful adaptive strategy to improve the efficiency of a control chart. In monitoring the coefficient of variation (CV), this strategy has been recently combined with various types of charts, including exponentially weighted moving average (EWMA) and variable sample size (VSS) charts. These combinations lead to desirable control charts with an impressive performance in detecting process shifts. However, in these studies, the authors asserted that adaptive type charts are not competitive to monitor downward shifts in the CV. As a consequence, they willingly omitted the decrease in process shifts. In this paper, we suggest overcoming this downside by designing two one-sided VSI CUSUM control charts for tracking the CV. The performance of the proposed charts is evaluated by the average time to signal (ATS) criterion. The numerical results show that our proposed adaptive type charts are actually efficient charts to monitor downward shifts in the CV.