The Morse-Pekeris oscillator model for the calculation of the vibration-rotation energy levels of diatomic molecules is revisited. This model is based on the realization of a second-order exponential expansion of the centrifugal term about the minimum of the vibrational Morse oscillator and the subsequent analytical resolution of the resulting approximate radial eigenvalue equation for the rotating Morse oscillator. It is, however, possible to develop the Morse-Pekeris model by transforming the second-order exponential expansion of the rotating Morse oscillator into an effective Morse oscillator and by then taking advantage of the well-known solutions for the Morse oscillator. Such a transformation can be carried out in a straightforward and instructive way merely by making a suitable change of variable of the internuclear coordinate. In addition, this alternative method allows us to correct the Morse-Pekeris model by simple use of first-order perturbation theory. The efficiency of this treatment is demonstrated by carrying out a numerical application to the H[subscript 2] molecule. (Contains 1 figure and 3 tables.)