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We present a broad and detailed study of the background components of a liquid scintillation (LS) detector, using a simple laboratory-built system, ICELS. It was specifically designed for radiocarbon dating and is compact and easily transportable (total weight 35 kg). Its flexible LS detector unit has a dome-shaped vial with 3 mL benzene to which 45 mg butyl-PBD is added. The vial sits on the top of a vertical 28-mm-diameter phototube. The gamma radiation, to which the benzene is exposed under varying conditions, was measured by replacing the vial with a 38-mm-diameter Nal crystal. The pulse-height spectra of the 14C LS background and the Nal gamma background were measured in a surface laboratory and in a deep underground counting room with: 1) a lead shield of varying thickness; 2) lead of normal and low 210Pb concentration; 3) phototubes of 2 different types; and 4) varying benzene volume. The beta emission from the face of the tubes was measured with a low-level Geiger counter.