The vibrational dependence of the intermolecular potential of Ar-HF is investigated through the spectra of levels correlating with HF(v = 3). We have previously reported measurements of the (vbKn) = (3000), (3100), and (3110) levels of Ar-HF using intracavity laser-induced fluorescence in a slit supersonic jet [J. Chem. Phys. 98, 2497 (1993)]. These levels are found to be well reproduced (within 0.1 cm-1) by the Ar-HF H6(4,3,2) potential [J. Chem. Phys. 96, 6752 (1992)]. The second overtone experiments are extended to include the (3002) state which is coupled to (31 10) through Coriolis interaction, and the (3210) state which is more sensitive to higher-order anisotropic terms in the potential. The observations establish that the level (3002) lies 0.229 cm-1 below (3110), with upper state rotational constant B = 0.085 89 cm-1. This is in good accord with the predictions of the H6(4,3,2) potential. The (3210) state lies at 11 484.745 cm-1 with B = 0.099 79 cm-1. The band origin is 1.7 cm-1 higher than predicted, and thus contains important new information on the vibrational dependence of the potential. Several detailed features of the spectra can be explained using the H6(4,3,2) potential. The Q-branch lines of the (3210) - (0000) band show evidence of a weak perturbation, which can be explained in terms of mixing with the (3112) state. The (3210) spectrum exhibits parity-dependent rotational predissociation and the widths of the P- and R-branch lines and the magnitude of the 1-type doubling can be explained in terms of coupling to the (3200) state, which is estimated to lie 4 cm-1 below the (3210) state. The Q-branch lines show a predissociation cutoff above Q (16); this is in reasonable agreement with the predictions of the H6(4,3,2) potential, but suggests that the binding energy calculated for the potential may be about 1 cm-1 too large. To examine the potential further, high-level ab initio calculations are performed, with an efficient basis set incorporating bond functions. The calculations give a well depth of 92%-95% of that of the H6(4,3,2) potential at theta = 0-degrees for v = 0 and v = 3, respectively; this is in line with earlier results on rare gas pairs. The calculations also reproduce the anisotropy of the H6(4,3,2) potential and its vibrational dependence. The dependence of the intermolecular potential on HF bond length is found explicitly.