The effects of pressure anisotropy and backstreaming heat flux on the fast and slow shock jump conditions are studied parametrically. The fast shock jump condition can be brought into agreement with earth bow shock observation by (1) q1q2 for Alfv¿n Mach number M&Agr;>10 in the quasi-perpendicular shock region (&thgr;BN>45¿) where q1 and q2 are the magnitude of the backstreaming heat flux on the upstream and downstream sides, respectively and &thgr;BN is the angle between the upstream magnetic field and the shock normal. The slow shock jump condition is insensitive to the heat flux. However, slow shocks cease to exist if p∥=p⊥ upstream and p∥>p⊥ downstream where p∥ and p⊥ are the pressure parallel and perpendicular to the local magnetic field. The minimum critical Mach number imposed by the entropy principle is shown to increase from unity as q1 becomes increasingly greater than q2.