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We have performed new direct-potential-fit (DPF) analyses of the rotationally resolved A1Πu (v ′ = 2, 3; J′ = 1, 2) → X1∑+g (v′′ ∈ [0, 10]; J ′′ ∈ [0, 3]) stimulated emission pumping spectra of Be2 [1] using two quite different analytical potential energy functions which incorporate the correct theoretically-known long-range behavior in different ways. These functions are: the damped Morse/long-range (MLR) potential [2] and the Chebyshev polynomial expansion (CPE) potential [3]. In contrast with the potential energy function determined in the original DPF analysis of Merritt et al., both of our functions unambiguously support the existence of the v = 11 last vibrational level which is bound by only 0.50(5) cm−1. These empirical potentials predict the equilibrium distance re = 2.444(1) and the dissociation energy De = 934.8(0.3) cm−1, values which are both remarkably close (within the uncertainties) with the best ab initio estimates.