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A comprehensive model study of Bose-Einstein correlation radii in heavy ioncollisions is presented. The starting point is a longitudinally andtransversally expanding fireball, represented at freeze-out by an azimuthallysymmetric emission function. The freeze-out temperature is allowed to featuretransverse and temporal gradients. Their effects on the correlation radii arestudied. In particular, we evaluate numerically their dependence on thetransverse mass of the particle pairs and check a recent suggestion, based onanalytical approximations, that for certain reasonable source parameters allthree correlation radii satisfy simultaneously a 1/\sqrt{M_\perp} scaling.Comment: 22 pages, 8 figures, epsf; replaced with the revised first part of  the original study, the revised second part (concerning opaque sources) can  be found under nucl-th/980501

Fine-tuning two-particle interferometry I: Effects from temperature gradients in the source