During collaborative learning, computer-supported or otherwise, students balance task-oriented goals with the interpersonal goals of relationship-building. This means that in peer tutoring, some pedagogically beneficial behaviors may be avoided by peer tutors due to their likelihood to get in the way of relationship-building. In this paper, we explore how the interpersonal closeness between students in a peer tutoring dyad and the peer tutors' instructional self-efficacy impacts those tutors' delivery style of various tutoring moves, and explore the impact those tutoring move delivery styles have on their partners' learning. We found that tutors with lower social closeness with their tutees provide more positive feedback to their tutee and use more indirect instructions and comprehension-monitoring, but this is only the case for tutors with greater tutoring self-efficacy. And in fact, those tutees solved more problems and learned more when their tutors hedged instructions and comprehension-monitoring, respectively. We found no effect of hedging for dyads with greater social closeness, on the other hand, suggesting that interpersonal closeness may reduce the face-threat of direct instructions and comprehension-monitoring, and hence reduce the need for indirectness, while tutors' instructional self-efficacy allows tutors to use those moves without feeling threatened themselves. These results emphasize that designers of CSCL systems should understand the nature of how the interpersonal closeness between collaborating students intersects with those students' self-efficacy to impact the use and delivery of their learning behaviors, in order to best support them in collaborating effectively.