The present paper (re)derives current sheet equilibrium solutions on the basis of the so-called kappa distribution functions for the particles. The present work builds upon a recent paper [W.-Z. Fu and L.-N. Hau, Phys. Plasmas 12, 070701 (2005)], where the authors formulated the equilibrium current sheet model with the kappa distribution. According to their work, however, the global temperature profile monotonically increases in the asymptotic regime. In the present paper it is shown that the presence of a finite stationary background population of the particles arrests the unlimited increase of the global temperature profile in the asymptotic limit. The present paper further extends the analysis by considering a current sheet model where the electron current is embedded within a thicker ion current layer, and where there exists a weak electrostatic potential drop across the current sheet. (c) 2006 American Institute of Physics.