In contrast to most diblock copolymers which exhibit the classical upper critical ordering transition (UCOT), polystyrene-b-poly n-butyl methacrylate-PS-b-PBMA-has been shown to undergo ordering upon heating through a lower critical ordering transition(LCOT). Here we report the phase behavior of a family of diblock copolymers formed from styrene and a homologous series of n-alkyl methacrylates, as determined by combined dynamic rheological testing and small-angle neutron scattering (SANS). It is shown that the shortest side chain methacrylates, with the exception of methyl methacrylate, exhibit the LCOT, while for side chains longer than n-butyl, the copolymers exhibit the classical UCOT behavior. Combined group contribution/lattice fluid model calculations of the solubility parameter and specific volume of the corresponding homopolymers qualitatively support these observations. The same calculations were further employed to molecularly design LCOT behavior into a new diblock material consisting of styrene and a random copolymer of methyl and lauryl methacrylate, denoted PS-b-P(MMA-r-LMA). The success of this approach suggests a simple semiquantitative method for predicting and designing the phase behavior of weakly interacting polymer pairs.