The rupee trimmed its initial losses, but was still trading down by 5 paise at 61 rupees 59 paise against the dollar in late morning deals today. This was attributed to demand for the green currency on the back of higher dollar overseas. After shedding 1 paise to close at 61 rupees 54 paise on Friday, the domestic currency fell by 12 paise to 61 rupees 66 paise in opening trade today.