just what the name implies. They are men's hats with stingy, narrow brims. Dress hats have stingy brims, whether they're fedoras like the satin-lined Allesandro (with its mischievous alternating green and yellow striped trim) or the The Scala Sicily, a fur felt center dent fedora. Christy's has a woolen Rex that meets the definition and there are other walking hats I know that have brims of two inches or less -- in other words, stingy brims: I'm thinking here of The Jonathan Richard Original Irish Walking Hat made of an exceptional Irish tweed and sewn to perfection in Dublin. Trilby hats such as those worn by the well-heeled and fashion conscious, like The Rod Keenan Bow Tie fur felt fedora, and that long hair beaver fur felt dress hat named after our beloved President, The JFK, (not to mention The Sedgewick, Keenan's fur felt fedora with an elongated silhouette) have all been crafted on the stingy brim side.
Be forewarned: if there's no brim at all, you've been had.
Pork pie hats lend themselves to stingy brims and once you see the cashmere-smooth fur felt Gordon in bark brown (from Makins), 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 men's pork pie hat, 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, such as 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.