The last few years have seen an increasing use of sequential online mechanisms, instead of the traditional direct counterparts, in college admissions in countries such as Germany, Brazil, and China. We describe those, and identify shortcomings they have in terms of incentives and outcome properties. We introduce a new family of mechanisms for one-sided matching markets, which improve upon these shortcomings. Unlike most mechanisms available in the literature, which ask students for a full preference ranking over all colleges, they are instead sequentially asked to make choices or submit partial rankings from sets of colleges. These are used to produce, in each step, a tentative allocation. If at some point it is determined that a student cannot be accepted into a college anymore, then she is asked to make another choice among those which would tentatively accept her. Participants following the simple strategy of choosing the most preferred college in each step is a robust equilibrium that yields the Student Optimal Stable Matching.