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Edelbaum's approach to the optimization of low-thrust transfers is revisited and some simplifications are removed. The variation of the spacecraft mass due to the propellant consumption is considered in the case of constant thrust, and the corresponding numerical result is compared with Edelbaum's solution. The approach is then extended to consider variable specific impulse and thrust magnitude with constant power level. The payload increment is first computed maintaining Edelbaum's suboptimal control strategy (i.e., constant-thrust direction during each half-revolution). An analytical solution of the quasi-circular one-revolution transfer is then found using the optimal control of both the thrust direction and magnitude. The very-low-thrust multirevolution problem is easily solved by assembling many one-revolution basic trajectories; in particular, the transfer from a 28.5 deg inclined low Earth orbit to the equatorial geostationary orbit is considered. Exact numerical solutions for both constant and variable specific impulse have also been obtained using an indirect optimization method: the accuracy of the solution based on the quasi-circular approximation has been verified.