Some reasonable conjectures are made concerning the finite-temperature pair correlations of spins with anisotropic antiferromagnetic coupling. These conjectures provide a general description of the ordering. Using them together with the finite value of the zero-temperature susceptibility, one obtains S1<S3<<0<<S4<S2, where Sn=1-(-1)n+2l=1nl, l is the zero-temperature pair correlation, and is the infinite-l limit of |l|. Bonner and Fisher's finite-chain extrapolations for l are in agreement with this result. Using their values of l (l=1, 2, 3, 4, ) and the inequality, bounds are computed for 5. The further conjecture that the rate of decrease in the absolute value of the correlation with distance is monotonic leads to a contradiction near the Heisenberg limit. The role of in the inequality and its derivation is particularly interesting since the limit l followed by T0 of the pair correlation of spins separated by l-1 spins is probably zero and not. When the correlations approximate their zero-temperature value out to a distance such that || and decrease slowly thereafter with increasing separation, then T is approximately zero. © 1966 The American Physical Society.