Analytic three‐dimensional mirror equilibria are calculated from the tensor‐pressure fluid equations by means of an asymptotic expansion procedure. The class of equilibria described here is of interest to the minimum‐Bend cells of current tandem mirror experiments. It is shown that in the shallow‐well approximation, a small plasma pressure can produce a relative change of order unity in the vacuum magnetic well, thereby leading to interchange instability. In addition, if the axial dependence of the quadrupole field is not chosen in a specific way, ’’long thin’’ corrections set an upper limit on the maximum allowable plasma radius. The proper choice of quadrupole field to avoid this limitation is discussed, and an analytic expression is derived for the interchange beta limit.