The temperature T_e(s) and density structure n_e(s) of active region loops in EUV observed with TRACE is modeled with a multithread model, synthesized from the summed emission of many loop threads that have a distribution of maximum temperatures and that satisfy the steady state Rosner-Tucker-Vaiana (RTV) scaling law, modified by Serio et al. for gravitational stratification (called RTVS_p in the following). In a recent Letter, Reale & Peres demonstrated that this method can explain the almost isothermal appearance of TRACE loops (observed by Lenz et al.) as derived from the filter-ratio method. From model-fitting of the 171 and 195 Å fluxes of 41 loops, which have loop half-lengths in the range of L = 4-320 Mm, we find that (1) the EUV loops consist of near-isothermal loop threads with substantially smaller temperature gradients than are predicted by the RTVS_p model; (2) the loop base pressure, p₀ ≈ 0.3 ± 0.1 dynes cm^-2, is independent of the loop length L, and it agrees with the RTVS_p model for the shortest loops but exceeds the RTVS_p model up to a factor of 35 for the largest loops; and (3) the pressure scale height is consistent with hydrostatic equilibrium for the shortest loops but exceeds the temperature scale height up to a factor of ≈3 for the largest loops. The data indicate that cool EUV loops in the temperature range of T_e ≈ 0.8-1.6 MK cannot be explained with the static steady state RTVS_p model in terms of uniform heating but are fully consistent with Serio's model in the case of nonuniform heating (RTVS_ph), with heating scale heights in the range of s_H = 17 ± 6 Mm. This heating function provides almost uniform heating for small loops (L 20 Mm), but restricts heating to the footpoints of large loops (L ≈ 50-300 Mm).