The morphologies of several styrene-isoprene miktoarm star copolymers have been examined by small angle x-ray scattering and electron microscopy. Three of these polymers were of the three-armed A(2)B type, and six were four-armed A(3)B miktoarms. The ordered microphase-separated morphologies displayed by these polymers were seen to be highly dependent on the architecture of the chains, and were quire different from those that occur in the corresponding linear block copolymers. These results can be quite well explained by a theory of Milner which is based on the bending energy of the microphase interface and the ability of the chains to stretch away from the interface between the microphases. We speculate that the small differences between the observations and theoretical predictions are due to the effects of the compression of chains in small gaps between adjacent domains.