The statistical efficiency of human observers in diagnostic tasks is an important measure of how effectively task relevant information in the image is being utilized. Most efficiency studies have investigated efficiency in terms of contrast or size effects. In many cases, malignant lesions will have similar contrast to normal or benign objects, but can be distinguished by properties of their boundary. We investigate this issue in the framework of malignant/benign discrimination tasks for the breast with ultrasound. In order to identify effects in terms of specific features and to control for other effects such as aberration or specular reflections, we simulate the formation of beam-formed radio-frequency (RF) data. We consider three tasks related to lesion boundaries including boundary eccentricity, boundary sharpness, and detection of boundary spiculations. We also consider standard detection and contrast discrimination tasks. We find that human observers exhibit surprisingly low efficiency with respect to the Ideal observer acting on RF data in boundary discrimination tasks (0.08%-3.3%), and that efficiency of human observers is substantially increased by Wiener-filtering RF frame data. We also find a limitation in efficiency is the computation of an envelope image from the RF data recorded by the transducer. Approximations to the Ideal observer acting on the envelope images indicate that humans may be substantially more efficient (10%-75%) with respect to the envelope Ideal observers. Our work suggests that significant diagnostic information may be lost in standard envelope processing in the formation of ultrasonic images.