The production of doubly charged Higgs bosons (H(+/-+/-)) at the CERN LHC can give rise to distinctive multi-lepton signatures. The discovery potential of H(+/-+/-) can be optimized by considering a search strategy which is sensitive to both of the dominant production mechanisms, q (q) over bar -> H(++) H(--) and q (q') over bar -> H(+/-+/-) H -/+. We compare the discovery potential for the signatures of exactly four leptons and at least three leptons in the final state, using the same set of cuts. We have carried out fast detector simulations at the LHC for both signal and backgrounds for a wide range of values of the charged Higgs mass. We find that the use of the latter channel can substantially improve the detection prospects of the doubly charged Higgs boson at the LHC.