We report an investigation of the scattering mechanisms affecting the two-dimensional electron system in modulation-doped Ga0.47In0.53As-Al0.48In0.52As single heterojunctions. Low-temperature magnetotransport measurements were used to determine the dependence of the electron mobility mu on the density N-s of the two-dimensional carriers. For N-s less than or equal to 4 X 10(11) cm(-2), we find that mu increases with N-s, leveling off as N-s is further increased. This behavior is a clear indication that, contrary to some theoretical predictions, mu is chiefly limited by ionized-impurity scattering in this regime. We develop a theoretical model of the scattering mechanisms present in our systems whose results agree with our experiments. We find that alloy and interface-roughness scattering become important only when N-s greater than or equal to 5 X 10(11) cm(-2). (C) 1996 American Institute of Physics.