The nature of coronal wave fronts is intensely debated. They are observed in several wavelength bands and are frequently interpreted as magnetosonic waves propagating in the lower solar atmosphere. However, they can also be attributed to the line-of-sight projection of the edges of coronal mass ejections. Therefore, estimating the altitude of these features is crucial for deciding in favor of one of these two interpretations. We took advantage of a set of observations obtained from two different view directions by the EUVI instrument onboard the STEREO mission on 7 December 2007 to derive the time evolution of the altitude of a coronal wave front. We developed a new technique to compute the altitude of the coronal wave and found that the altitude increased during the initial 5 min and then slightly decreased back to the low corona. We interpret the evolution of the altitude as follows: the increase in the altitude of the wave front is linked to the rise of a bubble-like structure depending on whether it is a magnetosonic wave front or a CME in the initial phase. During the second phase, the observed brightness of the wave front was mixed with the brightening of the underlying magnetic structures as the emission from the wave front faded because the plasma became diluted with altitude.