Are they enumerated with just initials?

Some census takers were plain lazy, some couldn’t spell, and some didn’t care.

After you have exhausted all the variations on your ancestor’s first and middle names, consider that they might have been enumerated with just their initials. Or perhaps their first initial and their middle name spelled out. I have seen entire townships where no one apparently had a first name and everyone was named with their initials. I have seen locations where census takers used initials for non-English names instead of trying to spell them correctly.

Maybe your ancestor was enumerated as J. Smith in the 1860 census. Now there’s a real problem.