Ga(In)N -based laser structures and related methods of fabrication are proposed where Ga (In)N-based semiconductor laser structures are formed on AlN or GaN substrates (20) in a manner that addresses the need to avoid undue tensile strain in the semiconductor structure. In accordance with one embodiment of the present invention, a Ga (In)N-based semiconductor laser is provided on an AlN or GaN substrate provided with an AlGaN lattice adjustment layer (30) where the substrate (20), the lattice adjustment layer (30), the lower cladding region (60), the active waveguiding region (40), the upper cladding region (50), and the N and P type contact regions (70, 60) of the laser form a compositional continuum in the semiconductor laser. Additional embodiments are disclosed and claimed.