The authors have shown previously that the maximum entropy method (MEM) forms a valuable tool for assisting in the estimation of surface amplitude distributions from reflected ultrasonic pulses. The surface inspection technique is extended to allow the determination of many common surface texture parameters from the amplitude distribution function. Using relatively accessible ultrasonic frequencies, surfaces in the practically important region of around 2 mu m to over 140 mu m roughness (Ra) are assessed. The MEM is used as a high-performance deconvolution technique to produce height amplitude distribution graphs with good resolution and low noise. From these graphs surface parameters such as Ra and Rq can be extracted. Three different types of machined surface and one layered surface are tested. In the latter two cases, the MEM is extended to allow negative points in its deconvolution image; the advantages of this move are described. Results from the use of 10 MHz and 40 MHz broadband plane compressional wave transducers are compared with those from a stylus instrument; good agreement is obtained. The difficulties of producing reliable results by both methods are summarized.