We present new high spatial resolution Very Large Telescope (VLT) and Very Large Array (VLA) observations of a sample of nine low-power (P1.4GHz <= 1025 WHz-1) radio hotspots. Infrared/optical emission is definitely detected in four of the nine observed objects, resulting in a detection rate of at least 45 per cent. This emission is interpreted as synchrotron radiation from the electrons accelerated in the hotspots. The integrated spectra of these hotspots reveal typical break frequencies between 105 and 106 GHz, two orders of magnitude higher than typically found in high-power hotspots. This supports the idea that in low-power hotspots with their relatively low magnetic field strengths, electrons emit most of their energy at higher frequencies. A simple spectral ageing analysis would imply that the emitting electrons have been injected into the hotspot volume less than ~103 years ago. We discuss possible scenarios to explain the lack of older electrons in the hotspot region. In particular, the extended morphology of the near-infrared/optical emission would suggest that efficient re-acceleration mechanisms rejuvenate the electron populations.