Embedded tense in Modern Greek (MG) displays an unexpected “optionality”: both present and past tenses can be used under a past tense attitude verb to convey a simultaneous reading. Building on Schlenker (1999) and Sharvit (2003, 2018), we claim that MG has a mixed tense system, being able to delete the embedded past like English and shift the embedded present like Russian and Hebrew. Thus, the correlation between having either a deleted past or a shiftable present but not both is accidental. This is theoretically important because it confirms that the two parameters are independent. We also complete the characterization of MG present tense in the cross-linguistic typology of embedded tense, claiming that it behaves like Russian and unlike Japanese, since our data suggest that it does not shift in non-attitudinal environments. Thus, we conclude that two parameters are active in attitudinal environments in MG: (i) a deleted past, and (ii) a shiftable present. Are these two the only routes to the simultaneous reading? There could in principle be a third one, namely interpreting the embedded past de re, i.e., with respect to the time of the utterance. However, we argue that this would over-generate simultaneous readings for languages without a deletion rule, such as Hebrew and Russian. We propose an analysis of the data based on Prefer De Se, predicting that there are indeed two roads to the simultaneous reading in MG.