In English, past tense stative clauses embedded under a past-marked attitude verb, like Eric thought that Kalina was sick, can receive two interpretations, differing on when the state of the complement is understood to hold, i.e. Kalina’s sickness precedes the time of Eric’s thinking (backward-shifted reading), or Kalina is sick at the time of Eric’s thinking (simultaneous reading). 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 only allow for the 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 not to be interpreted; and an implicature approach, which links the absence of such a reading to the presence of a “cessation” implicature associated with past tense. We report a series of experiments on Polish, which is commonly classified as a non-SOT language. First, we investigate the interpretation of complement clauses embedded under past-marked attitude verbs in Polish and English. This investigation revealed a difference between these two languages in the availability of simultaneous interpretations for past-under-past complement clauses, albeit not as large as a binary distinction between SOT and non-SOT languages would lead us to expect. We then address the question of whether the lower acceptability we observe for simultaneous readings in Polish might be due to an embedded cessation implicature. On the way to address this question, we show that in simple matrix clauses, Polish gives rise to the same cessation inference as English. Then we investigate 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, are a challenge for the implicature approach, and cast doubts on associating SOT phenomena with implicatures.