Rheological models based on molecular dynamics (as opposite to empirical relationships) are now preferred to link the molecular weight distribution (MWD) of linear polymers to their theological properties. These models incorporate the double reptation concept, which represents the relaxation modulus as an integral over the molecular weight distribution. We propose a method that incorporates a detailed modeling of all the relevant relaxation processes, including Rouse fast and longitudinal modes and glassy relaxation. In addition, we take into account the effect of polydispersity on the relaxation times for reptation, i.e., "'tube renewal." In order to demonstrate the importance of these features of our technique, we compare it with one involving the direct inversion of the double reptation integral without accounting for tube renewal and additional relaxation processes. To invert the relaxation modulus in terms of the molecular weight distribution, one must either solve the ill-posed problem using an efficient numerical algorithm or postulate a function to describe the MWD. The second approach is more robust and less sensitive to noisy data, but one must assume the form of the MWD a priori. We present a procedure for selecting this function and use it to compare the two approaches to inverting a G(t) model. Data for several binary blends and commercial polymers are analyzed using both approaches. We conclude that the more detailed technique is necessary when the MWD is broad or when there is a significant amount of low-molecular weight material present.