We present radial-velocity measurements obtained using high- and intermediate-resolution spectroscopic observations of the classical T Tauri star UZ Tau East from 1994 to 1996. We also provide measurements of Hα equivalent widths and optical veiling. Combining our radial-velocity data with those recently reported by Prato et al. (2002), we improve the orbital elements for this spectroscopic binary. The orbital period is 18.979±0.007 days and the eccentricity is e=0.14. We find variability in the Hα emission and veiling, signposts of accretion, but at periastron passage the accretion is not as clearly enhanced as in the case of the binary DQ Tau. The difference in the behaviour of these two binaries is consistent with the hydrodynamical models of accretion from circumbinary disks because UZ Tau East has lower eccentricity than DQ Tau. It seems that enhanced periastron accretion may occur only in systems with very high eccentricity (e>0.5). Based on observations made with the Isaac Newton Telescope, operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, the ESO 3.6-m telescope at La Silla Observatory in Chile, and the Shane 3-m telescope at Lick observatory in California.