In the committee coordination problem, a committee consists of a set of professors and committee meetings are synchronized, so that each professor participates in at most one committee meeting at a time. In this paper, we propose two snap-stabilizing distributed algorithms for the committee coordination. Snapstabilization is a versatile property which requires a distributed algorithm to efficiently tolerate transient faults. Indeed, after a finite number of such faults, a snap-stabilizing algorithm immediately operates correctly, without any external intervention. We design snap-stabilizing committee coordination algorithms enriched with some desirable properties related to concurrency, (weak) fairness, and a stronger synchronization mechanism called 2-Phase Discussion. In our setting, all processes are identical and each process has a unique identifier. The existing work in the literature has shown that (1) in general, fairness cannot be achieved in committee coordination, and (2) it becomes feasible if each professor waits for meetings infinitely often. Nevertheless, we show that even under this latter assumption, it is impossible to implement a fair solution that allows maximal concurrency. Hence, we propose two orthogonal snap-stabilizing algorithms, each satisfying 2-phase discussion, and either maximal concurrency or fairness. The algorithm that implements fairness requires that every professor waits for meetings infinitely often. Moreover, for this algorithm, we introduce and evaluate a new efficiency criterion called the degree of fair concurrency. This criterion shows that even if it does not satisfy maximal concurrency, our snap-stabilizing fair algorithm still allows a high level of concurrency.