Information frictions can harm the welfare of participants in two-sided matching markets. Consider a centralized admission, where colleges cannot observe students' preparedness for success in a particular major or degree program. Colleges choose between using simple, cheap admission criteria, e.g., high school grades as a proxy for preparedness, or screening all applications, which is time-consuming for both students and colleges. To address issues of fairness and welfare, we introduce two novel mechanisms that allow students to disclose private information voluntarily and thus only require partial screening. The mechanisms are based on Deferred Acceptance and preserve its core strategic properties of credible preference revelation, particularly ordinal strategy-proofness. In addition, we demonstrate conditions for which cardinal welfare improves for market participants compared to not screening. Intuitively, students and colleges benefit from voluntary information disclosure if public information about students correlates weakly with students' private information and the cost of processing disclosed information is sufficiently low. Finally, we present empirical evidence from the Danish higher education system that supports critical features of our model. Our work has policy implications for the mechanism design of large two-sided markets where information frictions are inherent.