The growth parameters of In(0.25)Ga(0.75)AS grown on GaAs by molecular beam epitaxy were investigated. Low substrate temperatures coupled with lower growth rates and low arsenic overpressures were explored and the corresponding threading dislocation densities were determined using transmission electron microscopy. Threading dislocation densities in layers much thicker than the critical thickness were found to be as low as 1x10(7) cm(-2) using optimal growth conditions. In addition, the critical thickness of the ternary alloy was estimated. The evolution of the misfit dislocations and threading dislocations was also examined as a function of epilayer thickness.