This paper describes a computational study of the directivity of noise radiated by jets with different nozzle exit geometries. The nozzles considered are both axisymmetric and nonaxisymmetric. Also, the study describes the differences between noise radiated from nozzles with planar and non-planar exits. Finally, jets with rectangular nozzles are considered. The Detached-Eddy Simulation (DES) approach is used to simulate both the jet nozzle internal and external flows as well as the jet plume development. This methodology allows the turbulence model to transition automatically from an unsteady Reynolds Averaged Navier-Stokes (URANS) method for attached boundary layers to a Large Eddy Simulation (LES) in separated regions. Thus it is ideally suited to jet flow simulations where the nozzle is included. Both cylindrical and Cartesian coordinate systems are used. The one equation Spalart-Allmaras turbulence model is used to describe the evolution of the turbulent eddy viscosity. An explicit 4th order Runge-Kutta time marching scheme is used. The far-field sound is calculated using the Ffowcs Williams-Hawkings permeable surface wave extrapolation method. This permits the noise to be predicted at large distances from the jet based on fluctuations in the jet's near field. This provides a good compromise between numerical accuracy and computational cost. Comparisons are made between predictions and measurements where they are available.