The Rupee today trimmed its early losses against the American currency after it fell by seven paise, to 62 rupees, 67 paise per dollar, on mild demand for the greenback from banks and importers on the back of higher dollar in overseas market.The rupee had resumed lower at 62 rupees, 80 paise per dollar as against the last closing level of 62 rupees, 60 paise per dollar.