Several technologically important alloys like Al-Li-Zr, Al-Li-Sc, Al-Sc-Zr, Al-Li-Sc-Zr, modified Inconel etc., exhibit compact precipitates in their microstructure. We present a phase-field model in two dimensions to study the morphological evolution of composite precipitates in ternary alloys. The model employs a modified regular solution description of the bulk free energy of the disordered matrix phase and ordered precipitates. Elastic strain energy of the three-phase system is described using Khachaturyan’s microelasticity theory. The temporal evolution of the spatially dependent field variables is determined by numerically solving coupled Cahn-Hilliard and Allen-Cahn equations for composition and order parameter fields, respectively. We systematically vary the misfit strains, alloy chemistry and mobilities of the diffusing species to study their effect on the development of compact precipitates. Compact core-shell morphology destabilizes when the precipitate phases have misfit strains of opposite signs with the matrix phase although the relative interfacial energies between the phases satisfy Cahn’s spontaneous wetting condition. Thus, the stability of “monodisperse” core-shell microstructures is determined by the interplay between the relative interfacial energies and elastic interactions between the phases. Further, our simulations show that low solute mobility within the core leads to sluggish coarsening of the compact particles.