We in­tro­duce a nov­el trans­mit­tance mod­el to im­prove the volu­met­ric rep­res­ent­a­tion of 3D scenes. The mod­el can rep­res­ent opaque sur­faces in the volu­met­ric light trans­port frame­work. Volu­met­ric rep­res­ent­a­tions are use­ful for com­plex scenes, and be­come in­creas­ingly pop­u­lar for level of de­tail and scene re­con­struc­tion. The tra­di­tion­al ex­po­nen­tial trans­mit­tance mod­el found in volu­met­ric light trans­port can­not cap­ture cor­rel­a­tions in vis­ib­il­ity across volume ele­ments. When rep­res­ent­ing opaque sur­faces as volu­met­ric dens­ity, this leads to both bloat­ing of sil­hou­ettes and light leak­ing ar­ti­facts. By in­tro­du­cing a para­met­ric non-ex­po­nen­tial trans­mit­tance mod­el, we are able to ap­prox­im­ate these cor­rel­a­tion ef­fects and sig­ni­fic­antly im­prove the ac­cur­acy of volu­met­ric ap­pear­ance rep­res­ent­a­tion of opaque scenes. Our para­met­ric trans­mit­tance mod­el can rep­res­ent a con­tinuum between the lin­ear trans­mit­tance that opaque sur­faces ex­hib­it and the tra­di­tion­al ex­po­nen­tial trans­mit­tance en­countered in par­ti­cip­at­ing me­dia and un­struc­tured geo­met­ries. This cov­ers a large part of the spec­trum of geo­met­ric struc­tures en­countered in com­plex scenes. In or­der to handle the spa­tially vary­ing trans­mit­tance cor­rel­a­tion ef­fects, we fur­ther ex­tend the the­ory of non-ex­po­nen­tial par­ti­cip­at­ing me­dia to a het­ero­gen­eous trans­mit­tance mod­el. Our mod­el is com­pact in stor­age and com­pu­ta­tion­ally ef­fi­cient both for eval­u­ation and for re­verse-mode gradi­ent com­pu­ta­tion. Ap­ply­ing our mod­el to op­tim­iz­a­tion al­gorithms yields sig­ni­fic­ant im­prove­ments in volu­met­ric scene ap­pear­ance qual­ity. We fur­ther show im­prove­ments for rel­ev­ant ap­plic­a­tions, such as scene ap­pear­ance pre­fil­ter­ing, im­age-based scene re­con­struc­tion us­ing dif­fer­en­ti­able ren­der­ing, neur­al rep­res­ent­a­tions, and com­pare it to a con­ven­tion­al ex­po­nen­tial mod­el.