We have searched 205 pb-1 of s =29 GeV data from the Mark II detector at the SLAC e+e- storage ring PEP for events which may signify the existence of a new lepton pair (L-,L0) where the L0 may be massive, but does not exceed the L- mass. Three event signatures for L+L- decay are examined: (i) e, (ii) (e or)(+4), and (iii) (e or )(3+0). The numbers of signature events are found to be in good agreement with Monte Carlo simulations of known background sources. The ranges of L- and L0 masses for which new lepton pairs are excluded are obtained using a likelihood-ratio method to compare the number of observed signature events to the expected background, and to the expected background plus Monte Carlo predictions of (L-,L0) signals. © 1989 The American Physical Society.