Online services collect personal data from their users, sometimes with no clear need. We studied how users sign-in to web sites using federated IDs, and found that most survey respondents were not aware of the data they expose. However, when presented with the tradeoffs behind each sign-in option, respondents reported a willingness to change how they sign-in to reduce their data exposure or, in fewer cases, to increase it to receive more benefits from the service. Our findings suggest that data exposure is a concern for users, and that there is a need for finding clearer ways for communicating it for each sign-in option.