The l-adic cohomology of Rapoport-Zink spaces is expected to realize local Langlands correspondences in many cases. Along this line is a conjecture by Harris, which roughly says that when the underlying Rapoport-Zink space is not basic, the l-adic cohomology of the space is parabolically induced. In this talk, we will discuss a result on this conjecture when the Rapoport-Zink space is of Hodge type and ``Hodge-Newton reducible''. The main strategy is to embed our Rapoport-Zink space to an appropriate space of EL type, for which the conjecture is already known to hold. If time permits, we will also discuss other applications of this strategy.