  So far, only one distribution function giving rise to a collisionless
nonlinear force-free current sheet equilibrium allowing for a plasma beta less
than one is known (Allanson et al., 2015; 2016). This distribution function can
only be expressed as an infinite series of Hermite functions with very slow
convergence and this makes its practical use cumbersome. It is the purpose of
this paper to present a general method that allows us to find distribution
functions consisting of a finite number of terms (therefore easier to use in
practice), but which still allow for current sheet equilibria that can, in
principle, have an arbitrarily low plasma beta. The method involves using known
solutions and transforming them into new solutions using transformations based
on taking integer powers ($N$) of one component of the pressure tensor. The
plasma beta of the current sheet corresponding to the transformed distribution
functions can then, in principle, have values as low as $1/N$. We present the
general form of the distribution functions for arbitrary $N$ and then, as a
specific example, discuss the case for $N=2$ in detail.
