An apparatus for breast imaging with x-rays comprising: an inflatable jacket configured for being removably secured to a compression paddle supported for movement toward a breast platform to compress a patient's breast between the paddle and the platform for imaging the breast with x-rays, said compression paddle having a front wall configured to be adjacent the patient's chest while the patient's breast is being imaged with x-rays, side walls extending transversely to the front wall, and an underside facing the breast platform; said inflatable jacket comprising a double-thickness bottom that extends along the underside of said compression paddle and forms at least one inflatable chamber, and front and side walls, which can be releasably secured to the compression paddle such that they extend along the front and side walls of the compression paddle; a fluid conduit that is in fluid flow communication with said inflatable chamber; and a fluid control unit coupled with said conduit and/or chamber to selectively inflate the chamber, wherein the inflated chamber remains between the compression paddle and the patient's breast for x-ray imaging of the breast, and wherein said inflatable jacket comprises two layers of flexible sheet material; characterized in that the two layers of flexible sheet material are fused or adhered to each other at a front wall and a side wall (18b,18c) of the inflatable jacket, but not at the bottom of the inflatable jacket, and that the two layers of flexible material are seamed at least at a portion that extends along a junction between the front wall and the underside of the compression paddle. an inflatable jacket configured for being removably secured to a compression paddle supported for movement toward a breast platform to compress a patient's breast between the paddle and the platform for imaging the breast with x-rays, said compression paddle having a front wall configured to be adjacent the patient's chest while the patient's breast is being imaged with x-rays, side walls extending transversely to the front wall, and an underside facing the breast platform; said inflatable jacket comprising a double-thickness bottom that extends along the underside of said compression paddle and forms at least one inflatable chamber, and front and side walls, which can be releasably secured to the compression paddle such that they extend along the front and side walls of the compression paddle; a fluid conduit that is in fluid flow communication with said inflatable chamber; and a fluid control unit coupled with said conduit and/or chamber to selectively inflate the chamber, wherein the inflated chamber remains between the compression paddle and the patient's breast for x-ray imaging of the breast, and wherein said inflatable jacket comprises two layers of flexible sheet material; characterized in that the two layers of flexible sheet material are fused or adhered to each other at a front wall and a side wall (18b,18c) of the inflatable jacket, but not at the bottom of the inflatable jacket, and that the two layers of flexible material are seamed at least at a portion that extends along a junction between the front wall and the underside of the compression paddle.