The speed [v(R)] of coronal mass ejections (CMEs) at various distances from the Sun is modeled (as proposed by Vrsnak and Gopalswamy in J. Geophys. Res. 107, 2002, doi: 10.1029/2001/JA000120 ) by using the equation of motion a drag=Îł(vâw) and its quadratic form a drag=Îł(vâw)|vâw|, where v and w are the speeds of the CME and solar wind, respectively. We assume that the parameter Îł can be expressed as Îł=αR ÎČ , where R is the heliocentric distance, and α and ÎČ are constants. We extend the analysis of Vrsnak and Gopalswamy to obtain a more detailed insight into the dependence of the CME SunâEarth transit time on the CME speed and the ambient solar-wind speed, for different combinations of α and ÎČ. In such a parameter-space analysis, the results obtained confirm that the CME transit time depends strongly on the state of the ambient solar wind. Specifically, we found that: i) for a particular set of values of α and ÎČ, a difference in the solar-wind speed causes larger transit-time differences at low CME speeds [v 0], than at high v 0; ii) the difference between transit times of slow and fast CMEs is larger at low solar-wind speed [w 0] than at high w 0; iii) transit times of fast CMEs are only slightly influenced by the solar-wind speed. The last item is especially important for space-weather forecasting, since it reduces the number of key parameters that determine the arrival time of fast CMEs, which tend to be more geo-effective than the slow ones. Finally, we compared the drag-based model results with the observational data for two CME samples, consisting of non-interacting and interacting CMEs (Manoharan et al. in J. Geophys. Res. 109, 2004). The comparison reveals that the model results are in better agreement with the observations for non-interacting events than for the interacting events. It was also found that for slow CMEs (v 0<500 km sâ1), there is a deviation between the observations and the model if slow-wind speeds (â 300 â 400 km sâ1) are taken for the model input. On the other hand, the model values and the observed data agree for both the slow and the fast CMEs if higher solar-wind speeds are assumed. It is also found that the quadratic form of the drag equation reproduces the observed transit times of fast CMEs better than the linear drag model.