Abstract Localised, nonspreading, wavelet solutions of the wave equation □ ϕ=0 with group velocity v> c and phase velocity u= c 2/ v< c are constructed explicitly by two different methods. Some recent experiments seem to find evidence for superluminal group velocities [J. Phys. I (Paris) 2 (1992) 1693; Phys. Rev. Lett. 68 (1992) 2421].