Fischer has shown how to compute a minimum weight spanning tree of degree at most $b Δ^* + \lceil \log\_b n\rceil$ in time $O(n^{4 + 1/\ln b})$ for any constant $b > 1$, where $Δ^*$ is the value of an optimal solution and $n$ is the number of nodes in the network. In this paper, we propose a distributed version of Fischer's algorithm that requires messages and time complexity $O(n^{2 + 1/\ln b})$, and O(n) space per node.