Prior work on fairness in machine learning has focused on settings where all the information needed about each individual is readily available. However, in many applications, further information may be acquired at a cost. For example, when assessing a customer's creditworthiness, a bank initially has access to a limited set of information but progressively improves the assessment by acquiring additional information before making a final decision. In such settings, we posit that a fair decision maker may want to ensure that decisions for all individuals are made with similar expected error rate, even if the features acquired for the individuals are different. We show that a set of carefully chosen confidence thresholds can not only effectively redistribute an information budget according to each individual's needs, but also serve to address individual and group fairness concerns simultaneously. Finally, using two public datasets, we confirm the effectiveness of our methods and investigate the limitations.