The paper examines property insurance contracts in which consumers choose t
he upper limit on coverage. Exclusions are of two types, and both reduce th
e demand for insurance of the included perils. A practical implication is t
hat an insurer can raise the demand for fire insurance by offering an earth
quake rider, and profit from the rider even when the premia are ceded in su
ch a way that the rider does not raise profit directly. The results do not
require assumptions about correlations between included and excluded losses
, which is interesting because correlations are decisive in most of the oth
er literature on background risk.