The paper is a continuation of the study of collisionless instabilities due to particle trapping. Particular attention is paid to the effects which promote stabilization of this instability. The author considers in detail the influence of: 1. unequal ion and electron temperatures; 2. finite orbits; 3. circulating particles; 4. temperature gradient. It is found that it is extremely difficult to achieve complete stabilization of 'trapped-particle' instabilities. However, the various stabilizing factors affect the instability most strongly when the particles have different temperatures