“Natural Language Equilibrium I” studies the effect of a commonly understood language on signaling game equilibria under the convention that off-path statements are interpreted as true unless they can be seen as a rational attempt to deceive. With this convention it was shown that, generically, only stable equilibrium outcomes of the setting with language can arise. Here, we strengthen the convention by also requiring that any statement must be interpreted as true according to its literal meaning unless doing so would make it profitable to use the statement deceptively. This strengthening refines equilibria even in pure communication games.