Ultrasonic flaw sizing is critical in nondestructive evaluation. However, the data available for sizing are often quite limited. For example, it is common to have a single pulse-echo (back scattered) wavetrain of limited bandwidth: i.e. it contains wavelengths that are comparable to and larger than the dimensions of the flaw. On the other hand a fair amount is often known about the nature of the expected range of flaws. It may be known that the flaw is a void, or a crack or an inclusion of a certain material type. In addition the expected shape for a flaw may be known (e.g. the flaw may be known to be a spherical flaw of unknown radius). The problem is then to determine the relevant unknown features of the flaw from the available data.