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In Magri 2009a, I argue that a sentence such as '#Some Italians come from a warm country' sounds odd because it triggers the scalar implicature that not all Italians come from a warm country, which mismatches with the piece of common knowledge that all Italians come from the same country. If this proposal is on the right track, then oddness can be used as a diagnostic for scalar implicatures. In this paper, I use this diagnostic to provide one more argument that scalar implicatures are computed not only at the matrix level but also in embedded position. The argument is based on a puzzling pattern of oddness in downward entailing environments. Some apparently unrelated facts about restrictions on temporal modification with individual-level predicates are shown to fit into the pattern.