FIR/HCN vs. HCN/CO ratios (left) and FIR/CO vs. HCN/CO (right) ratios for our sample, other high-z DSFGs and selected z ∼ 0 galaxies (Gao & Solomon 2004b; García-Burillo et al. 2012); i.e. star-formation efficiency of the molecular/dense gas versus dense-gas fraction (modulo α_CO and α_HCN). The purple dashed/dotted lines indicate the Jiménez-Donaire et al. (2019) HCN-FIR relation ±1σ scatter. We calculate depletion times θ_dep using α_CO = 1.0 and α_HCN = 10.0 although the actual values vary a factor of a few between different galaxy populations. At a given FIR/CO ratio, DSFGs (and ULIRGs) are systematically offset towards lower HCN/CO. The coloured lines indicate the line ratios for the “normal”, “intermediate”, and “starburst” models of Krumholz & Thompson (2007) as a function of mean cloud density ⟨n⟩. The DSFG stack is consistent with the “normal” model and ⟨n⟩≤10³ cm⁻³, indicating that the bulk of molecular gas in DSFGs is at low densities and/or with a relatively low Mach number.