The vital importance of composition-dependent low-temperature opacity in low-mass ( M \leq 3 M _ { \odot } ) asymptotic giant branch ( AGB ) stellar models of metallicity Z \geq 0.001 has recently been demonstrated ( e.g . ) . Its significance to more metal-poor , intermediate mass ( M \geq 2.5 M _ { \odot } ) models has yet to be investigated . We show that its inclusion in lower-metallicity models ( [ Fe/H ] \leq - 2 ) is essential , and that there exists no threshold metallicity below which composition-dependent molecular opacity may be neglected . We find it to be crucial in all intermediate-mass models investigated ( [ Fe/H ] \leq - 2 and 2.5 \leq M / \text { M } _ { \odot } \leq 5 ) , because of the evolution of the surface chemistry , including the orders of magnitude increase in the abundance of molecule-forming species . Its effect on these models mirrors that previously reported for higher-metallicity models – increase in radius , decrease in T _ { \text } { eff } , faster mass loss , shorter thermally pulsing AGB lifetime , reduced enrichment in third dredge-up products ( by a factor of three to ten ) , and an increase in the mass limit for hot bottom burning . We show that the evolution of low-metallicity models with composition-dependent low-temperature opacity is relatively independent of initial metal abundance because its contribution to the opacity is far outweighed by changes due to dredge-up . Our results imply a significant reduction in the expected number of nitrogen-enhanced metal-poor stars , which may help explain their observed paucity . We note that these findings are partially a product of the macrophysics adopted in our models , in particular the mass loss rate which is strongly dependent on radius .