In engineering education, one-on-one tutoring is commonly used to stimulate learning. This study develops and refines a practical tutoring model. The model is based on naturalistic tutoring augmented with elements from cognitive theory that are specifically missing in naturalistic tutoring. A four-week case study of near-peer tutors in engineering dynamics suggested four findings. First, interactions should be based within the tutee's cognitive framework. Second, deep exploring of the tutee's pre-existing knowledge leads to tutoring within the tutee's cognitive framework. Third, four tutoring actions emerged that address learning needs while keeping the tutoring within the tutee's framework. These tutoring actions are: a) guided assistance in problem solving, b) prompting tutees to construct and reconstruct what they know, c) explicit problem structuring and, d) presenting new information only when needed. Fourth, deep exploring facilitates the development of strong rapport. The paper concludes with a presentation of a revised tutoring model.