A method and implementation are presented to achieve a thousand fold speed-up for seeking of large files in a commonly used compressed neuroimaging data format NIfTI. Such technologies are not currently available in this research field while they would make the everyday work for hundreds of researchers and experts much smoother and faster. The method includes the creation of a novel index structure for the compressed data in order to achieve the speed-up. With random seek simulations, we demonstrate that a speed-up of over hundred up to even five thousand can be reached compared to the currently available implementations. By configuring the index structure properly, one can set an operating point which optimizes the efficiency as speed-up versus index size according to the requirements by the user. For example, a thousand fold speed-up can be achieved with an index size of only about two percent of the original compressed data.