Large eddy simulations were performed and Lighthill's analogy applied in order to predict the noise induced by the flow of a turbulent boundary layer (ReD = 12,000 or Re-theta = 300) over an open cavity (length/depth = 1). The effects of three simple geometrical changes, namely lids at the upstream edge (C10 and C20) and a chamfered edge (C23) on the downstream side of the cavity, on the internal circulation flows and shear-layer flow oscillations were determined and their effectiveness in reducing flow-induced noise was assessed. These small modifications were found to weaken the circulating flows inside the cavity and to suppress the pressure fluctuations near its downstream edge. As the lid length increases, the turbulence intensity inside the cavity is suppressed. The acoustic sources are concentrated at the downstream edge. The wall pressure fluctuations at the fundamental frequency are slightly higher for C23. The energy densities at the fundamental frequency are lower by 87.5% (C10), 30% (C20), and 18.7% (C23) than that of C00. The contributions to the acoustic directivity patterns of the dipole and quadrupole sources are oriented toward 135 and 45 degrees respectively. The ratios of decrease of the dipole and quadrupole sources are 93% (C10), 39% (C20), and 23% (C23) with respect to C00.