Here is a marketing definition of Slim-Jims from

Catalog size measuring 61/8″ 3 111/2.” Slim-jims became popular among catalogers looking for a way to reduce postage and production costs when the slim-jim size was the largest size qualifying for letter-rate postage. The slim-jim format is still favored by catalogers seeking a way to differentiate themselves from other catalogs. The J. Peterman catalog used a slim-jim format.

There is an excellent, informative article here at PostCom, which is available to the public:
The article helps to dispel some of the myths and outright fallacies that exist around the USPS view of these types of mailers.  A must read!

Let me know if you have any questions,
Best wishes,