This paper discusses change detection in SAR time-series. First, several statistical properties of the coefficient of variation highlight its pertinence for change detection. Subsequently, several criteria are proposed. The coefficient of variation is suggested to detect any kind of change. Furthermore, several criteria that are based on ratios of coefficients of variations are proposed to detect long events, such as construction test sites, or point-event, such as vehicles. These detection methods are first evaluated on theoretical statistical simulations to determine the scenarios where they can deliver the best results. The simulations demonstrate the greater sensitivity of the coefficient of variation to speckle mixtures, as in the case of agricultural plots. Conversely, they also demonstrate the greater specificity of the other criteria for the cases addressed: very short event or longer-term changes. Subsequently, detection performance is assessed on real data for different types of scenes and sensors (Sentinel-1, UAVSAR). In particular, a quantitative evaluation is performed with a comparison of our solutions with baseline methods. The proposed criteria achieve the best performance, with reduced computational complexity. On Sentinel-1 images containing mainly construction test sites, our best criterion reaches a probability of change detection of 90% for a false alarm rate that is equal to 5%. On UAVSAR images containing boats, the criteria proposed for short events achieve a probability of detection equal to 90% of all pixels belonging to the boats, for a false alarm rate that is equal to 2%.