The room temperature shot noise of a resonant tunneling diode was determined from microwave measurements as a function of bias. An AlAs/GaAs structure with multiple quasibound well states and asymmetric barrier thicknesses was investigated over a bias regime exceeding the first resonance. In contrast to results for single well state devices, significant noise suppression below the classical limit was also observed for bias ranges beyond the first resonance level. This suppression can be explained by competition between the first and second resonance levels for the thick barrier on the emitter side and due to predominately single barrier tunneling in the reverse polarity. ©1997 American Institute of Physics.