The present work investigates whether a noun's gender can be assigned on the basis of a relationship between the noun and a possessor, in a way that is expected (in principle) from independent lines of research on grammatical gender and possession, each of which attribute importance to projections low within the nominal domain. Evidence is provided from four unrelated languages supporting this possibility: from Teop (Austronesian, Oceanic), Jarawara (Arawan), Yanyuwa (Pama-Nyungan), and Coastal Marind (Trans-New Guinea, Anim). The proposal is that gender features on a nominalizing head can be conditioned locally, specifically by elements within nP, and not by structurally higher elements. This proposal captures an asymmetry between inalienable possessors, which have been argued to have a tight structural relationship with their possessee, and alienable possessors, which have been argued to be introduced by a higher Poss head. This asymmetry is observed in the languages investigated here, in which only inalienable possession appears to influence possessee gender. Beyond possession, the proposal captures an asymmetry observed in the literature for the influence of number features on assignment, and makes further predictions concerning the inability of other elements to influence assignment. The proposal consequently calls into question the viability of analyses that allow a noun's gender to be valued 'at a distance' via Agree. Broadly, the present work sheds light on what types of elements can be relevant to gender assignment, as well as on underexplored possession-, agreement-, and gender-related phenomena.