Virgin's website offers what were formerly "Saver Half" tickets, since simplication they became Off Peak Singles, but they are not available singly (this is quite simple and to avoid confusion). They are supposed to be given as one half of a return booking, with the other half an Advance single. They are only valid on one day so it's not as good to have two of them compared to an Off Peak return.
Perhaps the most simple ticket in the country is the many examples of Off Peak Single that are valid on any scheduled train and are not available singly? The name Saver Half obviously is complicated, so giving them a name that reflects the fact they are not available singly and that they are valid at peak time, ie Off Peak Single, is obviously a sensible move. ATOC and the DfT should be applauded for allowing this to happen, and Passenger Focus should be proud that they had the idea for it.