A compact homogeneous space M=G/K with dim(K)>0 is called aligned when its third Betti number is maximal, in the sense that b_3=s-1 if G has s simple factors. We will give formulas for the Ricci curvature of G-invariant metrics on aligned spaces and, as an application, study the existence and classification of Einstein metrics. This may be considered as a first raid into the largely unexplored class of all homogeneous spaces of compact non-simple Lie groups.