Drop the Last Name When Searching?

Have you considered dropping the last name when searching for an ancestor in a census or other record? This is especially a good idea for a relative who went by three names and whose middle name closely resembles a surname.

John Michael Trautvetter could have been enumerated as John Michael.

My ancestor Henry Jacobs Fecht is listed as Henry Jacobs in the 1870 census. Took me a while to find him listed like that.

Just something to consider if the usual search attempts do not pan out.