Within the minimal supersymmetric extension of the Standard Model, the
best fit to the most recent precision-measurement data requires charg
inos and neutralinos, with dominant Higgsino components and with masse
s within the reach of LEP1.5 (root s = 140 GeV). In this work, we pres
ent a detailed analysis of the neutralino and chargino production proc
esses for the favoured region of parameter space, that is low values o
f \mu\ and either low or large values of tan beta. We find that chargi
no and neutralino searches can cover the Higgsino region in the (mu, M
(2)) plane for values of M(2) less than or similar to 1 TeV, at the ne
xt phases of the LEP collider. We also show that, due mainly to phase-
space constraints, the lightest neutralinos should be more easily dete
ctable than charginos in most of the parameter space preferred by prec
ision-measurement data.