We present a new quantitative development of the reptation picture of de Gennes-Doi-Edwards. It is well-known that the original reptation theory is unable to fit linear relaxation spectra (G' and G") as it misses several important physical processes: (1) contour length fluctuations, (2) constraint release, and (3) longitudinal stress relaxation: along the tube. All of these processes were treated theoretically before; however, the treatment used either uncontrolled approximations or failed to include all of them at the same time. The aim of this work is to combine self-consistent theories for contour length fluctuations and constraint release with reptation theory. First, we improve the treatment of contour length fluctuations using a combined theoretical and stochastic simulation approach. This allows us to obtain an expression for the single chain relaxation function mu(t) without any adjustable parameters and approximations. To include constraint release, we use the scheme proposed by Rubinstein and Colby, which provides an algorithm for calculating the full relaxation function G(t) from the single chain relaxation mu(t). Then longitudinal modes are added, and a detailed comparison with different experimental data is given. One of the conclusions is that polystyrene is described by theory very well, but polybutadiene shows problems, which may be a first indication of nonuniversality of polymer dynamics.