  The selfgenerated wave fluctuations are particularly interesting in the solar
wind and magnetospheric plasmas, where Coulomb collisions are rare and cannot
explain the observed states of quasi-equilibrium. Linear theory predicts that
the firehose and the ordinary-mode instabilities can develop under the same
conditions, confusing the role of these instabilities in conditioning the
space-plasma properties. The hierarchy of these two instabilities is
reconsidered here for nonstreaming plasmas with an electron temperature
anisotropy $T_\parallel > T_\perp$, where $\parallel$ and $\perp$ denote
directions with respect to the local mean magnetic field. In addition to the
previous comparative analysis, here the entire 3D wave-vector spectrum of the
competing instabilities is investigated, paying particular attention to the
oblique firehose instability and the relatively poorly known ordinary-mode
instability. Results show a dominance of the oblique firehose instability with
a threshold lower than the parallel firehose instability and lower than the
ordinary-mode instability. For larger anisotropies, the ordinary mode can grow
faster, with maximum growth rates exceeding the ones of the oblique firehose
instability. In contrast to previous studies that claimed a possible activity
of the ordinary-mode in the small $\beta [< 1]$ regimes, here it is rigorously
shown that only the large $\beta [> 1]$ regimes are susceptible to these
instabilities.
