A class of algorithms for solving multistage stochastic recourse problems is described. The scenario tree is decomposed using a covering collection of subtrees. The approach is illustrated with two examples: adapting the diagonal quadratic approximation algorithm and adapting nested Bender's decomposition. The approach leads to a class of methods based on the subtree cover chosen (including the original implementation of the algorithm adapted). This approach increases flexibility in the size, number and structure of subproblems for multistage stochastic programming decomposition methods.