Magnetic resonance (MR) imaging methods with good spatial and contrast resolution are often too slow to follow the uptake of contrast agents with the desired temporal resolution. Imaging can be accelerated by skipping the acquisition of data normally taken with strong phase-encoding gradients, restricting acquisition to weak-gradient data only. If the usual procedure of substituting zeroes for the missing data is followed, blurring results. Substituting instead reference data taken before or well after contrast agent injection reduces this problem. Volunteer and patient images obtained by using such reference data show that imaging can be usefully accelerated severalfold. Cortical and medullary regions of interest and whole kidney regions were studied, and both gradient- and spin-echo images are shown. The method is believed to be compatible with other acceleration methods such as half-Fourier reconstruction and reading of more than one line of k space per excitation.