A framework for the construction of a hierarchy of explicit low-dispersion, low anisotropy FDTD algorithms is developed herein. The framework allows for the separation of dispersive and anisotropic effects due to a given explicit FDTD model construction using an extended stencil on a Yee-type staggered grid. Isotropic low-dispersion (2,4) and (4,4) FDTD algorithms are constructed by eliminating second-and fourth-order errors due to dispersion and anisotropy. The dispersive and anisotropic performance of these algorithms is compared to previously published schemes that fit within this hierarchical structure. The algorithms are examined for propagation of a wave pulse in an electrically large domain.