Just a correction re: the SSDI -- It is NOT an index of everyone that has died with a SSN. It only lists those people with SSNs whose deaths have been reported to the Social Security Administration.
See this link:http://search.ancestry.com/oldsearch/rectype/vital/ssdi/faq....
Also, here's a direct quote from the SSA: "The Death Index contains a listing of persons who had a Social Security number, who are deceased, and WHOSE DEATH WAS REPOTED to the Social Security Administration."http://www.ssa.gov/history/hfaq.html
For one reason or another, not ALL deaths are reported to the SSA.