Dynamic contrast-enhanced (DCE) MRI is a powerful technique to probe an area of interest in the body. Here a temporally constrained reconstruction (TCR) technique that requires less k-space data over time to obtain good-quality reconstructed images is proposed. This approach can be used to improve the spatial or temporal resolution, or increase the coverage of the object of interest. The method jointly reconstructs the space-time data iteratively with a temporal constraint in order to resolve aliasing. The method was implemented and its feasibility tested on DCE myocardial perfusion data with little or no motion. The results obtained from sparse k-space data using the TCR method were compared with results obtained with a sliding-window (SW) method and from full data using the standard inverse Fourier transform (IFT) reconstruction. Acceleration factors of 5 (R = 5) were achieved without a significant loss in image quality. Mean improvements of 28 +/- 4% in the signal-to-noise ratio (SNR) and 14 +/- 4% in the contrast-to-noise ratio (CNR) were observed in the images reconstructed using the TCR method on sparse data (R = 5) compared to the standard IFT reconstructions from full data for the perfusion datasets. The method has the potential to improve dynamic myocardial perfusion imaging and also to reconstruct other sparse dynamic MR acquisitions.