  In collision-poor plasmas from space, e.g., the solar wind and planetary
magnetospheres, the kinetic anisotropy of the plasma particles is expected to
be regulated by the kinetic instabilities. Driven by an excess of ion (proton)
temperature perpendicular to the magnetic field $(~T_\perp >T_\parallel)$, the
electromagnetic ion-cyclotron (EMIC) instability is fast enough to constrain
the proton anisotropy, but the observations do not conform to the instability
thresholds predicted by the standard theory for bi-Maxwellian models of the
plasma particles. This paper presents an extended investigation of the EMIC
instability in the presence of suprathermal electrons which are ubiquitous in
these environments. The analysis is based on the kinetic (Vlasov-Maxwell)
theory assuming that both species, protons and electrons, may be anisotropic,
and the EMIC unstable solutions are derived numerically providing an accurate
description for conditions typically encountered in space plasmas. The effects
of suprathermal populations are triggered by the electron anisotropy and the
temperature contrast between electrons and protons. For certain conditions the
anisotropy thresholds exceed the limits of the proton anisotropy measured in
the solar wind considerably restraining the unstable regimes of the EMIC modes.
