The distribution of the average north-south magnetic field component ⟨Bz⟩ in the vicinity of the neutral sheet has been investigated. This component is crucial for mappings between the nightside polar ionosphere and the equatorial magnetosphere. Data sets consisting of ~0.5 RE averages of magnetic field observations by the IMP/HEOS and ISEE spacecraft have been compared to the field predicted by the Tsyganenko models T87 and T89. In agreement with recent studies by C. Huang (data with 4-s resolution), it was found that both T87 and T89 underestimate ⟨Bz⟩ in the near tail region (xGSM=-10 to -22 RE) by as much as a factor of 2. Modified versions of the T87 model, incorporating plasma sheet warping, were obtained by fitting the model parameters via nonlinear least squares to the ISEE data set and yielded ⟨Bz⟩ values in agreement with the ISEE data. The study reveals an enormous scatter among the observed baseline values of ⟨Bz⟩ (on a time scale of 10--20 min), as well as intrinsic biases imposed by the mathematical structure of tail models, and these two factors (especially the first one) greatly limit the accuracy of model predictions of tail ⟨Bz⟩. In order to reduce the second factor, a localized tail model has been developed and was used to explore the spatial variations of ⟨Bz⟩. Comparisons between observations and models, both global and local, are presented. Finally, suggested guidelines for use of existing models and limitations of their use are discussed. ¿ American Geophysical Union 1993