Suppressing Deceased Constituents

Hello, we're having some troubles in suppressing deceased constituents and I'm hoping someone will be able to offer some assistance. We've been trying for quite some time now to figure out a way to suppress individuals who are deceased and households where BOTH members are deceased from lists and extractions. The way we've gone about it is to suppress any record where A1 is marked as deceased (as any household with a living member should have that member in the A1 position). Unfortunately, this suppresses any record in which one person is marked as deceased, even if the A1 constituent is not marked as such. We currently are not marking deceased individuals as inactive, but I know that's any option. Does anyone know of any pros or cons that go along with marking deceased constituents as inactive, especially within a household that has a living member? I assume it would not disrupt pulling the living member of that household, correct? And does anyone know why pulling on A1 Status = Deceased pulls in households with a living member? Thanks, Colleen