This paper studies the design effect of counting rules, for linking deaths to housing units where they are enumerated in the survey, on the sampling variance of dual system and single system estimators of death registration completeness. It investigates estimators based on conventional rules that uniquely link each death to a single housing unit as well as estimators based on multiplicity rules which permit deaths to be linked to more than one housing unit. Sampling variance formulas are derived containing parameters that reflect the efficiency of the counting rule. Estimates of these parameters for different counting rules are compared utilizing information that was collected in a mortality survey experiment. Finally, the design of a national death registration test is considered and the sample size implications of different counting rules arc compared.