Combined saccade-vergence movements result when gaze shifts are made to targets that differ both in direction and in depth from the momentary fixation point. Currently, there are two rivaling schemes to explain these eye movements. According to the first, such eye movements are due to a combination of a conjugate saccadic command and a symmetric vergence command; the two commands are not taken to be independent but instead are suggested to interact in a nonlinear manner, which leads to an intra-saccadic facilitation of the vergence command. According to the second scheme, the saccade generator is disconjugate, thus encoding vergence information in the saccadic commands themselves, and the remaining vergence requirement is provided by an asymmetric mechanism. Here, we test the scheme that suggests an intra-saccadic facilitation of the vergence command. We analyze this scheme and show that it has two fundamental properties. The first is that the vergence command is always symmetric, even during the intra-saccadic facilitation. The second is that the facilitated (and symmetric) vergence command sums linearly with the conjugate saccadic command at the final common pathway. Taking these properties together, this scheme predicts that the total magnitude of the saccadic component of combined saccade-vergence movements can be decomposed into a conjugate part and a symmetric part. When we tested this prediction in combined saccade-vergence movements of humans, we found that it was not confirmed. Thus, our results are incompatible with the facilitation of the vergence command hypothesis. Although these results do not directly verify the rivaling hypothesis, which suggests a disconjugate saccade generator, they do provide it with indirect support.