We describe observations of Neptune carried out using the James Clerk Maxwell Telescope (Mauna Kea, Hawaii) during September 1998. High-quality data for the sub-mm-wavelength rotational transitions of HCN ( $J=4{-}3$) and CO ( $J=3{-}2$ and 4-3) were obtained, and we use the data to make improved determinations of the abundances of these trace species and the temperature profile of Neptune's atmosphere.