First-principle approaches to the design of medical ultrasonic imaging systems for specific visual tasks are being explored in this paper. Our study focuses on breast cancer diagnosis and is based on the ideal observer concept for visual discrimination tasks, whereby tasks based on five clinical features are expressed mathematically as likelihood functions. Realistic approximations to the ideal strategy for each task are proposed as additional beamforming to maximize diagnostic image information content available to readers. Our previous study showed that a spatial Wiener filter (SWF) beamformer, derived as a stationary approximation of the ideal observer and operating on RF echo data, generally improved discriminability except for one case involving high-contrast lesions. This study explores an adaptive, iterative spatial Wiener filter (ISWF) beamformer that includes a lesion segmentation algorithm to overcome the stationarity assumption and improve discriminability for highcontrast lesions. Predicted performance is compared with that measured from trained human observers using psychophysical methods. We found the greatest feature enhancement of the delay-and-sum beamformer followed by SWF occurs at the image formation step where RF data are converted into B-mode data. The Smith-Wagner computational observer, which operates on the B-mode instead of RF data, was applied to indicate performance lost by envelope detection. ISWF was found to match the performance of SWF for low-contrast lesions and increase the performance for the high-contrast tasks. The ISWF beamforming approach offers greater diagnostic performance for discriminating malignant and benign breast lesions, and it provides a rational basis for further task-specific imaging system design.