In this paper an inverse method for converting linear viscoelastic properties of polymer melts into molecular weight distribution (MWD) is presented. It relies on the use of the double reptation mixing rule and the Generalized Exponential function (GEX) describing the MWD; i.e. an a priori knowledge of the nature of the solution is postulated following previous attempts (Nobile et al. 1996b; Nobile and Cocchini 1999, 2001) where the Tuminello kernel was adopted to get analytical results. Here a MWD dependent kernel, recently proposed in the literature (Thimm et al. 1999), is applied, still obtaining analytical results but avoiding the consequences of the crude step-like approximation of the Tuminello kernel. In particular, the steady-state compliance and the elastic modulus at small frequencies do not suffer from the underestimation discussed in the cited papers. At high frequencies, the Rouse modes contribution has also been considered in the model. The present approach turns out to be simpler, more accurate and robust than the previous one. Moreover, the results can be more clearly stated in the frame of the theory. Careful and easy-to-use formulas for the zero-shear-rate viscosity, the steady-state compliance, the modulus and frequency at the G'-G" crossover, have been obtained as a function of the MW averages. As expected, the comparison among the results obtained through the two kernels explicitly confirms the minor effects of the kernel on the rheology of polydisperse polymers. Concerning the molecular weight averages values, the predictions obtained from the dynamic moduli measurements typically differ less than 10% from those obtained from the reference measurements obtained with other methods.