CO excitation ladders for the three z > 6.5 QSO host galaxies studied here (filled squares), compared to other z ≳ 6 QSO hosts with CO(2–1) measurements (semi-transparent lines connected by small filled circles) and local AGN and QSO hosts from Rosenberg et al. (2015) and Kamenetzky et al. (2016; grey line and shading indicating the median and 16th to 84th percentiles). The colour-coding indicates the redshift, with the legend at the right providing the name of the corresponding QSO. Left panel: CO line luminosity ratios relative to CO(2–1). Right panel: CO line luminosities in units of L_⊙. Most z ≳ 6 QSO host galaxies show significantly (factor of ∼3×) higher mid-J versus CO(2–1) emission than the local AGN and QSO hosts (near/exceeding the thermalised value). The mid–J CO line emission for most z ≳ 6 QSO hosts exceeds that of the local AGN and QSO hosts by a greater factor than the CO(2–1) emission, implying that a greater fraction of these more massive molecular gas reservoirs is in more highly excited states.