Gender discrimination in hiring is a pertinent and persistent bias in society, and a common motivating example for exploring bias in NLP. However, the manifestation of gendered language in application materials has received limited attention. This paper investigates the framing of skills and background in CVs of self-identified men and women. We introduce a data set of 1.8K authentic, English-language, CVs from the US, covering 16 occupations, allowing us to partially control for the confound occupation-specific gender base rates. We find that (1) women use more verbs evoking impressions of low power; and (2) classifiers capture gender signal even after data balancing and removal of pronouns and named entities, and this holds for both transformer-based and linear classifiers.