Low-loss dielectrics are important technologically as insulators but there is little understanding of the physical causes of this property and even their spectral response is not well documented-this study has revealed a number of different types of behaviour which do not appear to have been recognised previously. Most low-loss materials show a "flat", nearly frequency-independent loss, but while some follow the "universal" fractional power law of frequency dependence which is widely applicable to more lossy materials, some are very different and require a fresh approach to their interpretation. It is pointed out that low-loss behaviour is not necessarily connected with the absence of impurity dipoles and the recently introduced concept of dipolar screening may explain low-loss behaviour in impure materials. The universal response is shown to be only one of several forms of dielectric behaviour and examples are given of possible alternative forms which may explain the apparent incompatibility of some experimental data with Kramers-Kronig relations.