In ocean acoustic tomography, acoustic travel times along multipaths between sources and receivers are inverted to obtain estimates of sound speed and currents in the region sampled by ray paths. Since the information gathered along ray paths is concentrated near their upper and lower turning depths, inversions are associated with a strong sidelobe in the vertical that is well separated from the main lobe. Thus there are three important measures of system performance, namely, resolution, variance, and sidelobe contamination. We criticize a methodology for investigating trade-off relations among these quantities that is based on a layered model of the medium. For N layers an N¿N resolution matrix specifies main lobe and sidelobe acceptance for each estimate. This matrix correctly represents resolution length and sidelobe contamination only when turning depths define layer interfaces. A resolution kernel is introduced that represents acceptance for a continuous medium. Because elements of the resolution matrix can be expressed as integrals over layers of the continuous resolution kernels, it is an intrinsic defect of the discrete approach that in forcing the resolution matrix close to the identity, it allows (and even encourages) cancellation of positive and negative acceptance within layers. This occurs for models with turning depths within layers. In such cases the resolution matrix may be virtually perfect, while true resolution properties are nevertheless pathologically degraded, and estimates do not in general approximate true layer averages. We also investigate the use in inversions of weightings derived from a priori knowledge and criticize the reporting of weighted rather than true sidelobe levels. ¿American Geophysical Union 1987