  We present the results of a spectroscopic monitoring campaign devoted to
three O-type stars in the Carina nebula. We derive the full SB2 orbital
solution of the binary system Tr 16-112, an exceptional dissymmetrical system
consisting of an O5.5-6V((f$^+$?p)) primary and a B2V-III secondary. We also
report on low-amplitude brightness variations in Tr 16-112 that are likely due
to the ellipsoidal shape of the O5.5-6 primary revolving in an eccentric orbit
around the system's centre of mass. We detect for the first time a clear SB2
binary signature in the spectrum of HD 93343 (O8 + O8), although our data are
not sufficient to establish an orbital solution. This system also displays low
amplitude photometric modulations. On the other hand, no indication of
multiplicity is found in the optical spectra of HD 93250. Finally, we discuss
the general properties of multiple massive stars in the Carina OB1 association.
