1. A device for compressing a patient's breast for scanning the breast with a motorized ultrasound transducer, comprising: a compression/scanning assembly including a frame and a breast compression sheet secured thereto, said sheet being made of an acoustically transparent and acoustic couplant permeable porous material, and said frame being configured for releasable attachment to an ultrasound imaging system, the compression/scanning assembly adapted to compress the patient's breast chestwardly and scan the breast through said sheet with the motorized ultrasound transducer moving across the breast; said sheet being taut at least in one direction when at rest but being partially conformable to locally deform when pressed against the patient's breast while the breast is being scanned therethrough with said motorized ultrasound transducer and said sheet is impregnated with an acoustic couplant; and said porous material being sufficiently sheer to view the compressed breast therethrough at least before said porous material is impregnated with said acoustic couplant; said porous material including a spatially-varying pore pattern that, when impregnated with said acoustic couplant during said scanning, promotes dissipation of air bubbles that might otherwise form between the breast and said scanning motorized ultrasound transducer, promoting locational stability of breast tissue being scanned, and flattening the breast when pressed against the breast with a selected force.