A 1975 J. Acoust. Soc. Am. article by Marcus and Carstensen [Marcus & Carstensen, ‘‘Problems with absorption measurements of inhomogeneous solids,’’ J. Acoust. Soc. Am. 52, 1334–1335 (1975)] reported perhaps the earliest study of potential artifacts in medical ultrasonics arising from phase‐cancellation effects at the face of a phase‐sensitive receiving transducer. This paper recognized the insights offered in a 1966 paper by Southgate [Southgate, ‘‘Use of power‐sensitive detector in pulse‐attenuation measurements,’’ J. Acoust Soc. Am. 39, 480–483 (1966)] proposing a phase‐insensitive receiver based on the acousto‐electric effect to reduce phase‐cancellation effects. Also in the 1970s, the Thurston lab at Duke and our lab in St. Louis examined consequences of propagating an ultrasonic field through the intrinsically inhomogeneous medium of soft tissue. Subsequently, several laboratories developed and implemented sophisticated algorithms applied to signals from receiving transducer arrays to provide some improvement. One of the most significant strides in reducing aberration artifacts came about serendipitously with harmonic mode (nonlinear) imaging. We will present experimental studies from our laboratory that examine approaches for reducing the profound effects arising from phase cancellation at the face of a phase‐sensitive receiving transducer on measurements of ultrasonic attenuation and backscatter. Measurements utilizing phase‐insensitive receiving transducers based on the acoustoelectric effect and measurement using two‐dimensional arrays of pointlike receivers to characterize tissue‐mimicking materials and intrinsically anisotropic hearts will be discussed. [Work supported by NIH R37‐HL40302 and R01‐HL72761.]