In the melon‐seed‐overpressure‐expansion (MSOE) model described by Siscoe et al. (2006) for the acceleration of coronal mass ejections (CMEs), magnetic repulsion force plays a central role. MSOE is a combination of Pneuman's (1984) melon seed concept with an overpressure expansion analytically formulated by Siscoe et al. (2006). The MSOE model creates a reduced formalism to describe CME acceleration and is highly advantageous for comparative studies. As originally presented, the MSOE model has the drawback of being able to produce only fast CMEs. For the work presented in this paper, we compare the acceleration of a 2.5‐D magnetohydrodynamics (MHD)‐modeled CME with that of a version of the MSOE model. On the basis of the results of the MHD simulations, we divide the acceleration of a CME into two phases: (1) a tethered phase before detachment (when the CME is tethered by external closed loops) and (2) a repulsion phase after detachment (when the tethering force that binds the CME is much smaller than outward magnetic repulsion force). We find that during the repulsion phase, the acceleration can be described well by the standard MSOE model. However, during the tethered phase, the CME acceleration is much slower than MSOE predictions. We therefore refine the MSOE model to include tethering and can account for both fast and slow CMEs with the final CME speed controlled by the CME detachment height.