One option out there from a few horn makers is a garland, an extra band of metal added to the edge of the bell near the rim. The idea is an old one; in this first photo is the garland on my Seraphinoff natural horn. Typical of older style garlands, it is over an inch wide. Besides being historically accurate to some period makers, it has two functions; to strengthen the edge of the bell and also to impact the sound of the horn.
Several makers use these on modern horns, one the most frequently seen being Schmid. Their horns are very light and distinctive in design (James Boldin gives a nice overview of why he purchased one recently here) and they are offered with as he notes “three different flare sizes and four different alloys.” One of those options being a garland, which they discuss briefly on their website as follows.
With or without garland?
With a weight of only 100 grams, the tastefully decorated garland from Engelbert Schmid does not deaden the sound. The garland causes a bit more resistance, and a somewhat rounder sound that gets brassy later, but more suddenly. Without the garland the transition to a brassy sound is more even. About 50 % of hornplayers sound better with the light garland from Engelbert Schmid.
From the text you can tell that it is something that is not easy to describe but, from helping a student who was testing Schmid bells recently, you can hear the difference. It is something that should be tried if you are looking at Schmid bells and it is not just bling, there is a difference that can be heard that is produced by the presence or absence of a garland.
A final note being this is just one variable of actually a dizzying number of variables that can be played with in the bell flare alone. Those variables among others involve type of metal, temper, thickness, spinning method, use of a bell wire, and the temper and material of the bell wire if it is present. Makers generally have an idea what they think is the best combination of those factors but options are offered as well. When offered a garland is worth considering by the advanced horn player.