I suppose this doesn't strictly speaking come under the category of "New Search Beta", but it's the sort of problem that periodically happens with New Search that never seemed to happen in Old Search.
1. First try. Go directly to the U.S. Federal Census Collection, go directly to 1910, and search exact for surname Cox in Jefferson County, Tennessee. There are no matches.
2. Second try. Do a global search and search exact for surname Cox in Jefferson County, Tennessee. There are lots of matches. Drill down to the U. S. Federal Census Collection and then to the 1910 census. There are 140 matches.
Needless to say, the results from the first try are not correct and the results from the second match are correct. Screen shots are attached.
P.S. It doesn't relate directly to the failure of the first search to find any Cox family members in Jefferson County, Tennessee in 1910 when manifestly there were a lot of Cox family members living in Jefferson County in 1910. But it still might be slightly interesting for me to explain why I was doing the search in the first place. The Cox family in Jefferson County is one of my major research interests, and I was going through some Jefferson County tombstone inscriptions for the Cox family.
One of them is for George C. Cox, born 14 Apr 1911, died 20 May 1911, son of Mr. and Mrs. B. T. Cox. I don't have anybody like that in my database, not even close. So I decided to see if I could find B. T. Cox in the 1910 census. I really wish I could search for B* Cox or for T* Cox, but I can't. So the next best thing is to search for all the Coxes and then to eyeball them to see if one of them looks like he might be B. T. Cox. It has been much discussed and I understand the reasons why searching for B* Cox or T* Cox would kill the performance of the ancestry.com servers. But that doesn't eliminate the need to do such searches. Searching for names that begin with a particular letter is such a frequent and a critical need, I wonder if there might be some way to implement it on the servers that doesn't go through the normal wildcard mechanism.
Also, I make note of the fact that you can go in the other direction. That is, you can search exact on Benjamin Cox with the option to display all the people named B. Cox. But you can't go in the other direction.