Q. Does the resulting rectangular or square cross section provide any advantageous difference in the way the cigar smokes (or ages)?
– Ben Olsen Jr.
A. This is a very good question. It started in Cuba and was done to keep the cigars from rolling off the table.* Don’t let anyone tell you differently, either. You can actually win a friendly bet on this one. 😉
The cigars were placed into a box that was somewhat smaller than what would normally accommodate the size being rolled, resulting in a square shape after the box was sealed.
With regard to your question, the square-pressed shape allegedly causes the cigar to burn longer; a result of the tobacco leaves being bunched even tighter together. It’s also supposed to make the cigar more flavorful. So, you could say that what started out as a way to keep cigars in their place while rolling, turned into one of those “happy accidents.”
Finally, cigars with very delicate wrappers like Connecticut shade and Cameroon are usually not box-pressed, because it can cause the wrapper leaf to crack.
* Source: The Ultimate Cigar Book by Richard Carelton Hacker