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Delay bandwidth products (DBPs) and physical pulselengths obtainable in media exhibiting electromagnetically induced transparency (EIT) are analyzed. The study is performed in stationary media as well as for dynamic storing of light pulses in such media. In the latter case, the dispersion inherent in storage and readout of the pulses is analyzed. It is shown that absorption and the group velocity dispersion (GVD) are limiting factors. Analytical expressions for the minimum compressed pulselength and DBP are derived, and these expressions show good agreement with simulations of pulse propagation in EIT media.