Low-frequency drain-current noise in pseudomorphic InAlAs/InGaAs/InP HEMTs has been studied at low drain bias as a function of the InGaAs pseudomorphic channel thickness. The 1/f noise at 77 K, quantified through the Kooge's empirical parameter alpha(ch), was found to be strongly dependent on the 2DEG concentration n(s) and correlated to the reciprocal mobility 1/mu. alpha(ch) was found to strongly increase at high channel thicknesses. Noise spectra analysis as a function of temperature reveals two traps with activation energies of 0.33 and 0.39 eV.