This paper reports on the synthesis and morphological characterization of graft, block copolymers in which a single polystyrene (PS) arm was grafted at an asymmetric position along a polyisoprene (PI) backbone. These materials represent a model series of asymmetric simple graft (ASG) block copolymer structures. The synthesis of these materials was carried out with methods developed for three-arm "miktoarm" star copolymers using anionic polymerization high-vacuum techniques with cholorosilane linking agents. The three arms were two polyisoprene blocks with different degrees of polymerization and one deuterated polystyrene block, which formed an asymmetric simple graft structure (ASG). Molecular characterization was performed using size exclusion chromatography (SEC) with refractive index and UV detection, membrane osmometry, and low-angle laser light scattering. These techniques confirmed that the materials exhibited narrow molecular weight distributions and low compositional heterogeneity. The morphologies formed by these samples were characterized using transmission electron microscopy (TEM) and small-angle neutron scattering(SANS). The ASG structures were compared with structures formed by Linear diblock copolymers and other samples having miktoarm structures, like I2S (symmetric simple graft with PI backbone and one PS branch grafted from the middle) and I3S (three equal PI arms and one PS arm). Comparisons of the morphologies formed and their dimensions indicated that the chain stretching and lateral crowding due to the miktoarm architecture was partially alleviated by the different lengths of PI blocks in ASG.