1. A tomosynthesis system comprising an anti-scatter grid that remains focused on the x-ray source in at least one dimension of the grid, said system further comprising: an x-ray source selectively emitting an imaging x-ray beam, a breast immobilizing structure defining a volume for a patient's breast, and an x-ray imaging receptor arranged such that said x-ray beam passes first through said volume and then through said anti-scatter grid before impinging on said imaging receptor; a source support mounting said x-ray source for selective movement relative to the breast immobilizing structure; an x-ray data acquisition control configured to: cause the x-ray source to move through a plurality of different imaging positions relative to the breast immobilizing structure and selectively illuminate said imaging receptor with said x-ray beam, and cause said imaging receptor to provide imaging data in response to being illuminated with said x-ray beam for said different imaging positions; wherein said anti-scatter grid remains focused on the x-ray source in at least one dimension of the grid while said x-ray source is moving through said different imaging positions; a processing and image reconstruction unit configured to receive and process said imaging data and obtain a plurality of projection images Tp and a plurality of reconstructed slices images Tr, wherein: each image Tp is a projection x-ray image of said volume taken with said x-ray beam for a respective one of said plurality of different positions of the x-ray source relative to the breast immobilizing structure; and each image Tr is an image of a respective 3-dimensional slice of said volume reconstructed through computer processing using at least several of said projection images Tp; and an image display unit configured to selectively display one or more of said slice images Tr and projection images Tp.