We investigate strong light confinement in high core-cladding index contrast waveguides with dimensions comparable to and smaller than the wavelength of incident light. We consider oval and rectangular cross sections and demonstrate that an optimal core size exists that maximizes the effective nonlinearity. We also determine that waveguides with asymmetrical cross sections provide the maximum possible nonlinearity, although only a small improvement over the symmetric case. Furthermore, we find that for a specified waveguide shape the largest nonlinearity occurs for nearly the same core area in all cases. Calculations of the dispersion for the optimal-size waveguide at a particular wavelength indicate that the group-velocity dispersion is normal. Ultimately, such designs could be used to develop low-power all-optical devices and to produce waveguides for ultra-low threshold nonlinear frequency generation such as supercontinuum generation.