Be forewarned: if there's no brim at all, you've been had.
Porkpies lend themselves to stingy brims and once you see the cashmere-smooth fur felt Makins Gordon in bark brown, I think you'll agree that the two-inch brim just had to be. Stacy Adams decreases the brim width a smidge with their Rocker porkpie, and then juxtaposes that with a generous 16 ligne grosgrain self band. Stingy brims are popular hats in Paris too, and Anthony Peto of France shows why with his unadorned Peto Stingy Brim and embossed Bastille pinch front hat. LA-based Mr. Green also has a thing for fur felt stingy brim dress hats for men, and when you peruse his handmade hats, The Frank, The Donald and The Fred, I think you'll develop a fetish yourself.
If you're a wool felt hat kind of guy looking for a briefer brim, the Dapper Dan with center dent from Stacy Adams will do quite nicely. The look is traditional but never stodgy, while Scala's Mad Hatter, a traditional top hat (with two-inch brim), is very dignified in appearance and at your ready for weddings, galas, and just impressing the hell out of everybody.
It's amazing how much difference an inch makes. Give or take.