In English, past tense stative clauses embedded under a past-marked attitude verb, like Eric thought that Kalina was sick, can receive two possible interpretations, differing on whether the state of the complement is understood to hold before, i.e. Kalina’s sickness precedes the time of Eric’s thinking, or at the matrix evaluation time, Kalina is sick at the time of Eric’s thinking. As is well known, the availability of the simultaneous reading – also called ‘Sequence of Tense’ (SOT) – is subject to cross-linguistic variation. Non-SOT-languages, like for instance Japanese or Polish, only allow for the other, backward-shifted interpretation. This cross-linguistic variation has been analysed in two main ways in the literature: A structural approach, connecting the availability of the simultaneous reading in a language to a syntactic mechanism that allows the embedded past morphology not to be interpreted, and an implicature approach, which links the absence of such reading to the presence of a ‘cessation’ implicature associated with past tense. We report an experimental study testing the predictions of the two approaches by investigating Polish past-under-past sentences in positive and negative contexts, comparing their potential cessation implicature to the exclusive implicature of disjunction. In our results, we found that the latter was endorsed more often in positive than in negative contexts, as expected, while the cessation implicature was endorsed overall very little, with no difference across contexts. The disanalogy between the disjunction and the temporal cases, and the insensitivity of the latter to monotonicity, is a challenge for the implicature approach, and casts doubts on associating SOT phenomena with implicatures. The results are instead in line with the structural approach, which expects no effect of monotonicity on the (un)availability of simultaneous readings, and no similarity between SOT phenomena and implicatures.