The demand for insurance against loss from a particular risky asset is likely to depend on other risks the decisionmaker faces. For independently distributed other risks, referred to as background risk, Eeckhoudt and Kimball [1992] determine the effect on insurance demand of introducing background risk. Recently, Eeckhoudt, Gollier, and Schlesinger [1996] determine conditions on preferences such that first- and second-degree stochastic deteriorations in background risk lead to a decrease in the decision-maker's willingness to accept other risks. These results, although formulated in a general decision model, also apply to insurance demand. This article continues analysis of this question by determining the effect on insurance demand of several other general changes in background risk.