The Randić index of a graph G is the sum of ((d(u))(d(v)))α over all edges uv of G, where d(v) denotes the degree of v in G, α≠0. When α=1, it is the weight of a graph. Delorme, Favaron, and Rautenbach characterized the trees with a given degree sequence with maximum weight, where the question of finding the tree that minimizes the weight is left open. In this note, we characterize the extremal trees with given degree sequence for the Randić index, thus answering the same question for weight. We also provide an algorithm to construct such trees.