Measurements from three classes of direct-drive implosions at the OMEGA laser system [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] were combined with Monte-Carlo simulations to investigate models for determining hot-fuel areal density (ρR hot ) in compressed, D 2 -filled capsules, and to assess the impact of mix and other factors on the determination of ρR hot . The results of the Monte-Carlo calculations were compared to predictions of simple commonly used models that use ratios of either secondary D 3 He proton yields or secondary DT neutron yields to primary DD neutron yields to provide estimates ρR hot,p or ρR hot,n , respectively, for ρR hot . For the first class of implosions, where ρR hot is low (≤ 3 mg/cm 2 ), ρR hot,p and ρR hot,n often agree with each other and are often good estimates of the actual ρR hot . For the second class of implosions, where ρR hot is of order 10 mg/cm 2 , ρR hot,p often underestimates the actual value due to secondary proton yield saturation. In addition, fuel-shell mix causes ρR hot,p to further underestimate, and ρR hot,n to overestimate, ρR hot . As a result, values of ρR hot,p and ρR hot,n can be interpreted as lower and upper limits, respectively. For the third class of implosions, involving cryogenic capsules, secondary protons and neutrons are produced mainly in the hot and cold fuel regions, respectively, and the effects of the mixing of hot and cold fuel must be taken into account when interpreting the values of ρR hot,p and ρR hot,n . From these data sets, we conclude that accurate inference of ρR hot requires comprehensive measurements in combination with detailed modeling. a) Also visiting Senior Scientist,