Thanks for the link, Bill D, but that site only gives sunrise and sunset times rounded to the nearest minute (just like the Naval Observatory site), which as I said is not precise enough to answer the question.
In response to TheBigPinkLad, the two nights to either side of the solstice *might* happen to be the same length, at least in some particular year, but I don't think it is "surely" the case.
It may depend on the exact time of day that the solstice occurs (as I understand it, we call Dec. 21, 2005 "the winter solstice" because the actual astronomical solstice occured *during* that day.)