Detailed near- and far-field acoustic measurements were conducted for two circular stepped nozzles with 30 deg and 60 deg design inclinations at over- and perfectly-expanded supersonic jet flow conditions and compared to those for a circular nonstepped nozzle. Far-field acoustic results show that stepped nozzles play an insignificant role in altering noise emissions at perfectly expanded condition. At an over-expanded condition, however, the longer stepped nozzle produces significant noise reductions at the sideline and upstream quadrants, while the shorter stepped nozzle does not. Noise spectra analysis and Schlieren visualizations show that noise reduction can be primarily attributed to mitigations in the broadband shock-associated noise (BSAN), due to the ability of the longer stepped nozzle in suppressing shock strengths at downstream region. Near-field acoustic measurements reveal that the source region, as well as the intensity of turbulent and shock noises, are highly sensitive to the stepped nozzle configuration. Furthermore, BSAN seems to be eliminated by the longer stepped nozzle in near-field region due to the shock structure modifications.