A central problem in recent research on speech production concerns the question to what extent speakers adapt their linguistic expressions to the needs of their addressees. It is claimed that speakers sometimes leak information about objects that are only visible for them and not for their listeners. Previous research only takes the occurrence of adjectives as evidence for the leakage of privileged information. The present study hypothesizes that leaked information is also encoded in the prosody of those adjectives. A production experiment elicited adjectives that leak information and adjectives that do not leak information. An acoustic analysis and prominence rating task showed that adjectives that leak information were uttered with a higher pitch and perceived as more prominent compared to adjectives that do not leak information. Furthermore, a guessing task suggested that the adjectives’ prosody relates to how listeners infer possible privileged information.