Today I received the death certificate for my great-great-grandfather's brother, Peter J. Burke, from the City of Buffalo. This also lists my great-great-great-grandfather as Patrick Burke, and it lists by great-great-great-grandmother as Nancy McNulty – my great-great-grandfather's listed her name as "Ann" not "Nancy".
It gives his date of birth. Perhaps someday I'll be able to use this to find some Irish records. I tried a copy of online search tools, but none turned up him or my great-great-grandfather.