The rupee trimmed its initial losses but was still quoted down by four paise to 62 rupees 35 paise against the dollar, on good demand for the greenback from banks and importers, on the back of firm dollar overseas. The domestic currency had opened steady at 62 rupees 30 paise today. The rupee had ended 13 paise higher at 62 rupees 31 paise against the dollar yesterday.