I wrote: > Mathematically, the best guess at the interval would > be 8 generations, but the range of plausible values goes from 2 to 50 > generations (based solely on the DNA comparison). After sending that message, I realized I had left out the follow-up. The original question was what whether the DNA results had shown that the Williams were *close* relatives in the usual sense, but there is more to be considered than that. The important thing is not the DNA test in isolation -- it's the combination of DNA and conventional research. Since we cannot ever expect to get DNA samples from the immigrant Williams, it will remain forever impossible to use "paternity test" technology to prove or disprove a *really* close relationship. However, we must remember the context of the DNA testing that has been done. We have demonstrated clearly that there are many different and "completely unrelated" Carpenter families. (Note that I have used quotes around that phrase to emphasize that only the male-line relationships are examined by the DNA project -- we cannot test for female connections.) Some of the Carpenters are of German origin and were originally Zimmermanns, but many are evidently English, and it is therefore remarkable that the two Williams are related at all. This is the "nugget" to carry away from the DNA testing. Bottom line: it is now all the more important to pursue the lines of conventional genealogical research for the immigrant Williams. If their respective families were well-to-do in the 15th and 16th centuries, we probably already have documentation of various sorts going back to their common ancestor. Therefore, the DNA tests give us reason to hope that the whole problem can be solved if only we can find proof of where the Williams themselves fit into the picture. John Chandler