  We discuss a family of Vlasov-Maxwell equilibrium distribution functions for
current sheet equilibria that are intermediate cases between the Harris sheet
and the force-free (or modified) Harris sheet. These equilibrium distribution
functions have potential applications to space and astrophysical plasmas. The
existence of these distribution function had been briefly discussed in by
Harrison and Neukirch 2009, but here it is shown that their approach runs into
problems in the limit where the guide field goes to zero. The nature of this
problem will be discussed and an alternative approach will be suggested that
avoids the problem. This is achieved by considering a slight variation of the
magnetic field profile, which allows a smooth transition between the Harris and
force-free Harris sheet cases.
