Sovereignty comes from the feudal system of medieval Europe where power flowed up pyramid-style. Historically, the political structure of Indian tribes has not been like a pyramid with most of the power concentrated in the hands of a few. Rather, tribes have been organized in clusters of families and clans or related families. When a group became too large, it split apart forming separate bands. Because sovereignty doesn't fit the natural organization of tribes, Deloria suggested adapting the idea of sovereignty to fit.
External sovereignty forms the basis for tribes as nations to deal with other political entities.
This is the context in which to understand treaties with the United States government and any local contracts or agreements that might come out of those treaties. External sovereignty can be applied to all external activities where the tribe acts as a single political entity. The important principle to remember, according to Deloria, is that to keep external sovereignty, you must maintain that you are a nation and that there is nationhood involved. In practical application, tribes need to identify their external activities and then decide at what level to negotiate with other political entities and with whom. Deloria expressed concern that tribes who regularly dealt with low level groups, such a conservation districts, instead of dealing with the highest executive official of an outside political group ran the risk of being perceived as a low level political group.