Following a recent numerical investigation of tonal noise radiation through two model scale coaxial exhaust configurations (typical of small and large turbofan engines), this paper presents additional computational results in an attempt to improve agreement with the measured data. In the experiments 'target' spinning modes were generated with a mode synthesizer located within a uniform annular section upstream of the exhaust nozzles. The in-duct complex mode amplitude of each propagating azimuthal/radial mode was measured with a dual axial array rotated in steps over 180°. The numerical method is based on the direct solution of the frequency-domain linearised Euler equations and uses the measured complex modal amplitudes to synthesise the modal source excitation at the in-flow boundary. The far-field sound is obtained via an open Kirchhoff surface just outside the jets. Previous comparisons of the radiated sound level directivities measured with polar and azimuthal microphone arrays with the directivities of the computed target modes revealed some discrepancies at various combinations of angle, frequency and flow condition. Additional calculations that take into account the next most dominant, non-target modes have yielded improved comparisons with the measured data. It is the purpose of the present paper to extend this study to include all the propagating modes in the comparisons with measured data for and to cover a wider range of frequencies and flow conditions typical of approach, cut-back and sideline conditions. The computed far-field radiation of (1) the target mode alone, (2) the sum of all the non-target cut-on modes and (3) all the cut-on modes are compared with the measurement. The results indicate that when the contributions from the non-target modes are included, significantly improved agreement with the measured data is usually achieved for the cases in which the directionalities of the target and non-target modes are really distinct. Even if experimentally generated modes are dominant within the duct, the far-field directivity is not necessarily dominated by these modes and comparing the computed radiation for the dominant mode with the experimental data may be misleading in terms of the prediction capability of the numerical method used. © 2011 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc.