We address the striking coexistence of localized waves (''pulses'') of
different lengths, which was observed in recent experiments and full
numerical simulations of binary-mixture convection. Using a set of ext
ended Ginzburg-Landau equations, we show that this multiplicity finds
a natural explanation in terms of the competition of two distinct, phy
sical localization mechanisms; one arises from dispersion and the othe
r from a concentration mode. This competition is absent in the standar
d Ginzburg-Landau equation. It may also be relevant in other waves cou
pled to a large-scale field.