Tutors often make use of explanations that do not promote learning. One reason for the ineffectiveness of explanations might lie in tutors' failure to take into account a tutee's understanding in order to individualize instruction. To test whether tutors provide more effective explanations when they are assisted in assessing a tutee's understanding, we conducted an experiment (N = 30 dyads of tutors and tutees) and varied whether tutors received information about a tutee's individual knowledge level. Results showed that only tutors provided with information about the tutee were able to customize instruction. As a consequence, the individualized explanations lowered the incidence of clarifying questions on the part of the tutees, deepened their understanding, and reduced the number of false beliefs about newly learned concepts. The findings suggest that a diagnosis-based approach to support tutors in developing a model of the tutee effectively contributes to the individualization of instruction in tutoring. (Contains 2 figures, 3 tables and 1 footnote.)