A method of reducing threading dislocation densities in non-polar such as a-{11-20} plane and m-{1-100} plane or semi-polar such as {10-1n} plane III-Nitrides by employing lateral epitaxial overgrowth from sidewalls of etched template material through a patterned mask. The method includes depositing a patterned mask on a template material such as a non-polar or semi polar GaN template, etching the template material down to various depths through openings in the mask, and growing non-polar or semi-polar III-Nitride by coalescing laterally from the tops of the sidewalls before the vertically growing material from the trench bottoms reaches the tops of the sidewalls. The coalesced features grow through the openings of the mask, and grow laterally over the dielectric mask until a fully coalesced continuous film is achieved.