There is a disagreement at the empirical level about the availability of non-maximal readings of plural definites in semantically negative grammatical environments. Some theories of definite plurals are built on the assumption that everything else being equal, non-maximal readings are equally available in positive and negative environments, while others assume that they are unavailable or less available in negative environments. What makes it difficult to settle this debate with introspective judgments is the fact that non-maximal readings are inherently context sensitive, and positive and negative sentences are typically used in different kinds of conversational contexts, so direct comparison of different sentences is not conclusive for adjudicating between the two views. This paper reports on three experiments that tested the availability of non-maximal readings in the scope of different quantificational expressions, every, no, not every, and exactly two. Crucially, we tested how two different background contexts affect truth-value judgments, instead of a direct comparison of truth-value judgments. Our results show that context has a robust effect for definite plurals under every and not every but a much smaller effect for definite plurals under no and exactly two. We claim that these findings pose different challenges for different theories of non-maximality in the current literature.