We study the possibility of exciting electromagnetic ion cyclotron waves (EICWs) in solar ejecta (CMEs) by a kinetic instability driven by ion temperature anisotropies. Our approach is to vary key parameters about assumed baseline values. Since Tp,∥>Tp,⊥ in most solar ejecta, the polarization of the unstable waves is right-handed. If the average proton beta is low (&bgr;p≤0.3), the activity is negligible for moderate temperature ratios, Tp,∥/Tp,⊥. Increasing &bgr;p increases both the frequency range and the instability growth rate. Increasing the temperature anisotropy brings about qualitatively similar effects as increasing &bgr;p, with comparable growth rates. Increasing the relative alpha-to-proton density ratio &eegr; has two effects: the active frequency range is shifted toward lower frequencies and the growth rate increases. Between &eegr;=0 and &eegr;=0.15, the maximum growth rate increases by a factor of ~20, highlighting the importance of the alphas for generating this instability. A case that may represent some magnetic clouds with exceptional parameters, &bgr;p=0.2, Tp,∥/Tp,⊥=10, and &eegr;=0.08--0.15, is considered. The maximum growth rate is found to be twice the reference CME case, while the active frequency range is 3 times wider. We conclude that EICWs should be present in some ejecta and possibly also in those magnetic clouds with relatively weak magnetic field, high He++ content, and large Tp,∥/Tp,⊥ ratios, and whose &bgr;p is high, for example, through interaction with a succeeding fast stream. We also suggest that substantial changes with respect to normal conditions should occur in the power spectrum of EICWs in the terrestrial plasma depletion layer when a CME, or a magnetic cloud, with negative anisotropy passes Earth. ¿ 1998 American Geophysical Union