How many roads are there to a simultaneous reading?

Past-under-past only sometimes yields simultaneous readings in non-Sequence of Tense (SOT) languages. I claim that a distinction should be made among non-SOT speakers. Indeed, only some of them get temporal de re readings of the embedded past. An analysis in terms of an individually parametrized Prefer Local Binding rule in the temporal domain is proposed, prioritizing logical forms with locally bound temporal variables. So, present-under-past temporal de se is preferred over past-under-past temporal de re to get simultaneous readings. Finally, interspeaker variation is predicted for SOT languages and a new diagnostic for temporal de re in SOT languages is developed.