The miscibility of polypropylene (PP) melts in which the chains differ only in stereochemical composition has been investigated by two different procedures. One approach used detailed local information from a Monte Carlo simulation of a single chain, and the other approach takes this information from a rotational isomeric state model devised decades ago, for another purpose. The first approach uses PRISM theory to deduce the intermolecular packing in the polymer blend, while the second approach uses a Monte Carlo simulation of a coarse-grained representation of independent chains, expressed on a high-coordination lattice. Both approaches find a positive energy change upon mixing isotactic PP (iPP) and syndiotactic PP (sPP) chains in the melt. This conclusion is qualitatively consistent with observations published recently by Mulhaupt and co-workers. The size of the energy change on mixing is smaller in the MC/PRISM approach than in the RIS/MC simulation, with the smaller energy change being in better agreement with the experiment. The RIS/MC simulation finds no demixing for iPP and atactic polypropylene (aPP) in the melt, consistent with several experimental observations in the literature. The demixing of the iPP/sPP blend may arise from attractive interactions in the sPP melt that are disrupted when the sPP chains are diluted with aPP or iPP chains.