Commensurated subgroups in finitely generated branch groups

A subgroup H <= G is commensurated if broken vertical bar H : H boolean AND gHg(-1)broken vertical bar < infinity for all g epsilon G. We show that a finitely generated branch group is just infinite if and only if every commensurated subgroup is either finite or of finite index. As a consequence, every commensurated subgroup of the Grigorchuk group and many other branch groups of independent interest is either finite or of finite index.