Separation of scattering properties ͑Lambert's ͒ from reflection properties ͑the reflection loss' angle derivative ␣͒ presents difficulties in the geoacoustic inversion of long range reverberation in isovelocity water, and here it is shown that there is still a problem in a refracting environment. An alternative technique is proposed where reverberation is modified by altering the source or receiver beam pattern, for instance, using a triplet array or ring source, to provide a dipole and monopole pattern. Combinations of these two measures of reverberation then conveniently determine ␣ and independently of other unknown quantities from long ͑or short͒ range data, in fact even from a single range. In addition the short range ratio of the two quantities determines the critical angle independently. The effects of refraction and other source or receiver beam patterns, including a horizontal beam and a tilted beam, are investigated by using analytical techniques. To enhance the credibility of these findings and demonstrate the benefits of the approach an example is posed as a standard inversion problem using a cost function based on both types of reverberation. Finally the technique is applied to some experimental data by forming simultaneous monopole and dipole beams in the vertical plane.