Suprathermal particle populations and loss-cone structures are the most common characteristics of ion and electron velocity distributions observed in space plasmas. We introduce a significant generalization of the family of kappa distributions to a suprathermal loss-cone distribution, applicable to a variety of space plasma modeling. On the basis of this concept a general mirror instability threshold criterion is derived from an energy principle for collisionless plasmas, covering the full range from two-temperature Maxwellians to complex loss-cone conditions occupied by high-energy ion species. We demonstrate that nonthermal plasma characteristics are the source of significant mirror instability threshold reduction where the specific structure of the velocity-space distribution dominates as a regulating mechanism for wave mode excitation. ¿ 2001 American Geophysical Union