Perfect (optical) vortex (PV) beams are fields whose radial profile is mooted to be independent of orbital angular momentum (OAM). To date, the best experimental approximation of these modes is obtained from passing Bessel-Gaussian beams through a Fourier lens. However, the OAM-dependent width of these quasi-PVs is not precisely known and is often understated. We address this here by deriving and experimentally confirming an explicit analytic expression for the second moment radius of quasi-PVs. We show that this width scales in proportion to ℓ in the best case, the same as most "regular" vortex modes, albeit with a much smaller proportionality constant. This Letter will be of interest to the large community who seek to use such structured light fields in various applications, including optical trapping, tweezing, and communications.