The Bowl Alliance at that time included the Orange Bowl, the Fiesta Bowl and the Sugar Bowl (Championship game in 1996). The Rose Bowl was clearly one of the top bowls, but not in the Bowl Alliance.

The other New Year's Day Bowls at that time were: Outback (#16 Alabama vs. #15 Michigan), Gator (#12 North Carolina vs. #25 West Virginia), Florida Citrus (#9 Tennessee vs. #11 Northwestern), and the Cotton (#5 BYU vs #14 Kansas State).

From a tradition standpoint the Cotton Bowl was played on New Year's Day starting in 1937 and was the home team was the winner of the SWC vs. (usually) the runner-up of the SEC. Later it became the home of the Big 12 Champion.

In 1996 it was pretty clearly the best non-Bowl Alliance game outside of the Rose Bowl. So, was it in the top 4? Nope. But it was pretty clearly number 5.

It was a big deal to be in the Cotton Bowl and BYU crashed the party as a member of the WAC that year. It was also a little bit of a downer, as many (at least BYU fans) felt that BYU should have been a part of the Bowl Alliance and invited to the Fiesta Bowl that year. This dream really got hosed by Texas when they upset Nebraska in the Big 12 title game and got an auto bid to the Fiesta Bowl ranked #20. Nebraska, ranked #6, got an at-large bid to the Orange Bowl and BYU was relegated to the spot outside the Bowl Alliance in the Cotton Bowl.