We present VLA 5-GHz and MERLIN 408-MHz observations of a sample of steep-spectrum low-frequency-variable sources. The radio observations show that the vast majority of sources have linear sizes typical of the compact steep spectrum sources. A classification based on their arcsecond-scale structure allows us to separate them into two classes, namely sources with an unresolved component and lobe-dominated sources. All but three sources show the existence of compact (subarcsecond) components which are required by models which explain the source variability as due to propagation effects in the interstellar medium. There are indications that the hotspots are the origin of the variability in lobe-dominated sources.