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In this paper, we develop an efficient method for designing the geometry of dielectric strip plasmonic structures for future subwavelength waveguiding applications. Leveraging an efficient finite-difference field solver, we investigate the impact of dielectric strip geometry on propagation loss and spatial light confinement. We demonstrate that a dielectric strip embedded in a metallic medium can support single-mode propagation while achieving subwavelength light confinement. We then formulate and solve the dielectric strip design optimization problem to ensure monomode propagation while balancing propagation losses and light confinement. The results indicate that the design technique can locate optimal dielectric strip geometries more efficiently than enumerating over the complete design space, which is crucial for the realization of subwavelength on-chip waveguiding applications.