Inability to detect vessel overlap and vascular loops can compromise the interpretation of magnetic resonance angiograms. A data-adaptive ray tracing (DART) technique was developed to produce the appropriate variations in signal intensity at points of vessel overlap in order to simulate the standard angiographic representation of vessels. In this technique a threshold is utilized to identify vessels in the image slices composing a 3D angiographic data set. A mask, which defines regions slightly larger than the vessel boundaries, is obtained by blurring the vessel information surviving the initial threshold. This mask is converted to binary form prior to multiplication by the original angiographic data set. Following application of an additional threshold to the masked data, line integrals through the regions defined by the mask are performed to obtain an angiographic signal proportional to the integrated vessel signal as in conventional angiography. This integrated reprojection is then uniquely combined with a maximum intensity pixel (MIP) reprojection to produce the final DART image. The application of the DART technique to 2D time-of-flight and 3D phase-contrast angiograms successfully enabled the identification of over-lapping vessels and vascular loops. DART was also found to produce less vessel narrowing than the MIP technique.