Routing protocols are at the core of distributed systems performances, especially in the presence of faults. A classical approach to this problem is to build a spanning tree of the distributed system. Numerous spanning tree construction algorithms depending on the optimized metric exist (total weight, height, distance with respect to a particular process, . . . ) both in fault-free and faulty environments. In this paper, we aim at optimizing the diameter of the spanning tree by constructing a minimum diameter spanning tree. We target environments subject to transient faults (i.e. faults of finite duration). Hence, we present a self-stabilizing algorithm for the minimum diameter spanning tree construction problem in the state model. Our protocol has the following attractive features. It is the first algorithm for this problem that operates under the unfair and distributed adversary (or daemon). In other words, no restriction is made on the asynchronous behavior of the system. Second, our algorithm needs only O (log n) bits of memory per process (where n is the number of processes), that improves the previous result by a factor n. These features are not achieved to the detriment of the convergence time, which stays polynomial.