The rupee fell by 34 paise to 55.99 against the US dollar in early trade at the Interbank Foreign Exchange market today as the American currency gained against other currencies overseas.Forex dealers said besides trengthening of dollar overseas, rupee fell for the fourth straight session on increased demand for the American currency from importers along with a weak opening in the domestic equity market.The rupee had ended lower by 31 paise at 55.65 against the dollar in the previous session on Tuesday on sustained dollar buying by importers and worries over higher trade deficit in July.