  We present a reanalysis of visible/near-infrared (480-930 nm) observations of
Neptune, made in 2018 with the MUSE instrument at the Very Large Telescope
(VLT) in Narrow Field Adaptive Optics mode, reported by Irwin et al., Icarus,
311, 2019. We find that the inferred variation of methane abundance with
latitude in our previous analysis, which was based on central meridian
observations only, underestimated the retrieval errors when compared with a
more complete assessment of Neptune's limb darkening. In addition, our previous
analysis introduced spurious latitudinal variability of both the abundance and
its uncertainty, which we reassess here. Our reanalysis of these data
incorporates the effects of limb-darkening based upon the Minnaert
approximation, which provides a much stronger constraint on the cloud structure
and methane mole fraction, makes better use of the available data and is more
computationally efficient. We find that away from discrete cloud features, the
observed reflectivity spectrum from 800-900 nm is very well approximated by a
background cloud model that is latitudinally varying, but zonally symmetric,
consisting of a H$_2$S cloud layer, based at 3.6-4.7 bar with variable opacity
and scale height, and a stratospheric haze. The background cloud model matches
the observed limb darkening seen at all wavelengths and latitudes and we find
that the mole fraction of methane at 2-4 bar, above the H$_2$S cloud, but below
the methane condensation level, varies from 4-6\% at the equator to 2-4\% at
near the south pole, consistent with previous analyses, with a equator/pole
ratio of $1.9 \pm 0.2$ for our assumed cloud/methane model. The spectra of
discrete cloudy regions are fitted, to a very good approximation, by the
addition of a single vertically thin methane ice cloud with opacity ranging
from 0 - 0.75 and pressure less than $\sim 0.4$ bar.
