  We reanalyze the results of the chargino searches at LEP (on the basis of the
DELPHI 189 GeV data sample), including the possibility of complex MSSM
parameters. We point out the possible differences between the complex- and
real-parameter analysis. We check that the regions excluded by ``standard''
analyses remain generally robust against the introduction of complex
parameters, with the exception of light sneutrino and low $\tan\beta$ scenario,
where additional constraints like those given by the $Z^0$ width or electric
dipole moment measurements are necessary.
