We present a phase method for ultrasonic thickness measurement of materials with significant attenuation and variants for its improvement in order to increase the efficiency of detection of informative signals and the accuracy of determining their time position. At present, composite materials have become widespread in various technical fields. Various methods, including acoustic, are used for their non-destructive testing. It should be noted that a large part of such materials has significant coefficients of attenuation of acoustic oscillations. Therefore, extending the capabilities of methods for ultrasonic thickness measurement of articles made from such materials is an important task. There are two ways that are proposed to improve the method: by using a combination of procedures for preliminary filtering of the investigated signals based on empirical mode decomposition and subsequent adaptive median filtering of r-statistics, as well as applying weight processing of r-statistics. We carried out computerized measurement experiments, which allowed the justification of choosing the aperture of a sliding window in the devised methods; we obtained dependences of signal/noise values of the initial informative characteristics on signal/noise values of the investigated signals. It is shown that the error in determining a time position of the detected echo impulses, when using the improved methods, is 1.5–2 times less than the error when the basic method is applied. The results obtained could be used for the development of new ultrasonic echo impulse thickness measurement devices with improved metrological characteristics.