The study contributes to the ongoing debate about the "privacy paradox" in the context of using social media. The presence of a privacy paradox is often declared if there is no relationship between users' information privacy concerns and their online self-disclosure. However, prior research has produced conflicting results. The novel contribution of this study is that we consider public and private self-disclosure separately. The data came from a cross-national survey of 1,500 Canadians. For the purposes of the study, we only examined the subset of 545 people who had at least one public account and one private account. Going beyond a single view of self-disclosure, we captured five dimensions of self-disclosure: Amount, Depth, Polarity, Accuracy, and Intent; and two aspects of privacy concerns: concerns about organizational and social threats. To examine the collected data, we used Partial Least Squares Structural Equation Modeling. Our research does not support the presence of a privacy paradox as we found a relationship between privacy concerns from organizational and social threats and most of the dimensions of self-disclosure (even if the relationship was weak). There was no difference between patterns of self-disclosure on private versus public accounts. Different privacy concerns may trigger different privacy protection responses and, thus, may interact with self-disclosure differently. Concerns about organizational threats increase awareness and accuracy while reducing amount and depth, while concerns about social threats reduce accuracy and awareness while increasing amount and depth.