Recent developments in the use of statistical energy analysis for the prediction of vibration levels on spacecraft components have led to the need to measure the frequency averaged modal density. In the case of structural components having low damping it has been extremely difficult to make a successful measurement by using existing techniques. Success has usually been achieved by the addition of damping tape to the structure under test. The transient testing technique also requires extremely long data lengths on lightly damped structures, which can lead to a requirement for Fourier transforms considerably longer than normally available. In the technique described here random excitation and extremely short data lengths are used; the technique is shown to give good results on structures with no additional damping material, with a considerable saving in time and expense not only during the experimentation but also during data processing.