Social Network Sites (SNS) are often characterized as a trade-off where users must give up privacy to gain social benefits. We investigated the alternative viewpoint that users gain the most benefits when SNSs give them the privacy they desire. Applying structural equation modeling to questionnaire data of 303 Facebook users, we examined the complex relationship between privacy and SNS benefits. We found that SNS users whose privacy desires were met reported higher levels of social connectedness (i.e., perceived relational closeness with others) than those who achieved less privacy than they desired. Social connectedness, in turn, played a pivotal role in building social capital (i.e., the benefits derived from relationships with others). These findings suggest that more openness may not always be better; SNSs should aim to achieve 'Privacy Fit' with user needs to enhance user experience and ensure sustained use.