We propose and study slot waveguide geometries where both quasi-TE and quasi-TM modes may propagate highly confined within the same low-index slot region. Conventional horizontal and vertical slot waveguides can only provide high slot confinement for either the quasi-TM or quasi-TE modes, respectively. Different two-dimensional slot waveguide structures are analyzed in terms of their mode characteristics, such as the effective index, the confinement factor, and the overlap of quasi-TE and -TM modes within the slot. Attention is also paid to practical manufacturability. Various waveguide structures can be tailored to have zero birefringence or equal confinement at both polarizations. Values for the confinement factors and the overlap of the two polarizations, in the slot region, can reach 0.4 to 0.5.