  We study the LHC discovery potential for heavy Majorana neutrino singlets in
the process pp -> W+ -> l+ N -> l+ l+ jj (l=e,mu) plus its charge conjugate.
With a fast detector simulation we show that backgrounds involving two
like-sign charged leptons are not negligible and, moreover, they cannot be
eliminated with simple sequential kinematical cuts. Using a likelihood analysis
it is shown that, for heavy neutrinos coupling only to the muon, LHC has 5
sigma sensitivity for masses up to 200 GeV in the final state mu+- mu+- jj.
This reduction in sensitivity, compared to previous parton-level estimates, is
driven by the ~ 10^2-10^3 times larger background. Limits are also provided for
e+- e+- jj and e+- mu+- jj final states, as well as for Tevatron. For heavy
Dirac neutrinos the prospects are worse because backgrounds involving two
opposite charge leptons are much larger. For this case, we study the
observability of the lepton flavour violating signal e+- mu-+ jj. As a
by-product of our analysis, heavy neutrino production has been implemented
within the ALPGEN framework.
