We present a multi-frequency study of radio relics associated with the galaxy clusters A4038, A1664, and A786. Radio images, integrated spectra, spectral index maps, and fits to the integrated spectra in the framework of the adiabatic compression model are presented. Images of the relic in A4038 at 150, 240, and 606 MHz with the Giant Meterwave Radio Telescope have revealed extended ultra-steep spectrum ( Delta *a ~ --1.8 to --2.7) emission of extent 210 X 80 kpc2. The model of passively evolving radio lobes compressed by a shock fits the integrated spectrum best. The relic with a circular morphology at the outskirts of the cluster A1664 has an integrated spectral index of ~ -- 1.10 ? 0.06 and is best fit by the model of radio lobes lurking for ~4 X 107 yr. The relic near A786 has a curved spectrum and is best fit by a model of radio lobes lurking for ~3 X 107 yr. At 4.7 GHz, a compact radio source, possibly the progenitor of the A786 relic, is detected near the center of the radio relic. The A786 radio relic is thus likely a lurking radio galaxy rather than a site of cosmological shock as has been considered in earlier studies.