It seems to be a common and intuitively plausible assumption that conversational implicatures arise only when one of the so-called conversational maxims is violated at the level of what is said. The basic idea behind this thesis is that, unless a maxim is violated at the level of what is said, nothing can trigger the search for an implicature. Thus, non-violating implicatures wouldn’t be calculable. This paper defends the view that some conversational implicatures arise even though no conversational maxim is violated at the level of what is said.