Dynamic MRI has proven to be an important tool in studies of transient physiologic changes in animals and humans. High sensitivity and temporal resolution in such measurements are critical for accurate estimation of dynamic information. Fast imaging, often involving expensive hardware, has evolved for use in such cases. We demonstrate herein the possibility of accelerated data acquisition schemes on conventional machines using standard pulse sequences for dynamic studies. This is achieved by combining reduced-encoded dynamic data (typically 30 to 40 phase encodings) with a priori high-resolution data via a novel constrained image reconstruction algorithm. Such an approach reduces image acquisition time significantly (by a factor of 3 to 4 in the examples described here) without loss in the accuracy of information.