Recent ALMA observations unveiled the structure of CO gas in the 23 Myr old ? Pictoris planetary system, a component that has been discovered in many similarly young debris discs. We here present ALMA CO J = 2-1 observations, at an improved spectro-spatial resolution and sensitivity compared to previous CO J = 3-2 observations. We find that (1) the CO clump is radially broad, favouring the resonant migration over the giant impact scenario for its dynamical origin, (2) the CO disc is vertically tilted compared to the main dust disc, at an angle consistent with the scattered light warp. We then use position-velocity diagrams to trace Keplerian radii in the orbital plane of the disc. Assuming a perfectly edge-on geometry, this shows a CO scaleheight increasing with radius as R0.75, and an electron density [derived from CO line ratios through non-local thermodynamic equilibrium (NLTE) analysis] in agreement with thermodynamical models. Furthermore, we show how observations of optically thin line ratios can solve the primordial versus secondary origin dichotomy in gas-bearing debris discs. As shown for ? Pictoris, subthermal (NLTE) CO excitation is symptomatic of H2 densities that are insufficient to shield
