A method for producing an image representative of the vasculature of a subject using a MRI system includes the acquisition of a signal indicative of a subject' cardiac phase. During each heartbeat of the subject, image slices of a volume covering a region of interest (ROI) within the subject are acquired by applying a volume-selective venous suppression pulse to suppress (a) venous signal for an upper slice in the ROI; (b) venous signal for slices that are upstream for venous flow in the ROI; and (c) background signal from the upstream slices. Next, a slice-selective background suppression pulse is applied to suppress background signal of the upper slice. Following a quiescent time interval, a spectrally selective fat suppression pulse is applied to the entire volume to attenuate signal from background fat signal. Then, a simultaneous multi-slice acquisition of the upper slice and the upstream slices is performed.