Q Card

BBM was not the only card manufacturer to debut in 1991.  A company called Q Card put out a set of 120 plastic cards with rounded corners (10 cards per team).  The cards were issued two to a pack, with a little window in the front of the pack to show you the team logo of the top card:

At 2 1/8 inches by 3 3/8 inches, the cards themselves were a little smaller than standard sized cards.  They are unnumbered (except for the uniform number), but there's this odd little seven digit number in the upper left corner of the card fronts - it reminds me of the serial numbers on menko cards that never really made any sense either.  Here's a couple example cards:

The card backs featured the statistical record of the player plus a small white rectangle that resembles the signature strip on the back of a credit card - I guess the intent was to have some place that a player could autograph the card.  Here's a sample back of Kenji Miyamoto of the Swallows:

Fighters Collection has a page devoted to the Fighters cards from the set.

I think these cards are pretty rare - I don't see them up on eBay very often.  In addition to the 120 card set, Q Card also issued a 62 card set for the 1991 All Star teams - exactly the same size as the BBM set and featuring the manager and coaches as well as the players.  These are the only two sets the company ever produced.