Mr. Kass, of Heaven Hill, said the bar owners “always want something different, something that others can’t get.”

Still, there are limits on what they can get. Heaven Hill offers only four of its whiskeys for sale as private barrels: Elijah Craig 12-year-old, Henry McKenna Single Barrel 10-year-old, and Evan Williams Single Barrel 10-year-old, all bourbons; and Bernheim, a wheat-based whiskey. Some buyers ask that the chosen barrel be bottled at a higher proof, which some think lends the liquor extra flavor. But Heaven Hill, protective of its products, typically doesn’t honor those requests.

“We won’t stray too far from our brand attributes,” Mr. Kass said.

Kris Comstock, the bourbon marketing director at Buffalo Trace, agreed. “You don’t want it to be wildly different” from what customers are used to, he said.

Beyond that, the whiskey makers aim to please. A visit to Heaven Hill to pick out a barrel begins in the rick house, or barrel warehouse, near the visitors’ center. The distillery offers the buyer a choice of three barrels. The casks are popped open and the deep amber liquor is fished out with a whiskey thief, a long cylindrical tool used to extract a small sampling of aging whiskey.

The customers are told everything about each whiskey: which rick house it came from, which floor of that rick house and its current proof. Tastes are compared and notes are taken. The whiskey is diluted to regular proof and tasted some more.

The Silver Dollar and Trick Dog recently went in on a barrel together. “There’s lots of discussion,” said Scott Baird, an owner of Trick Dog. “The first thing we learned was that everything smells great in the rick house. We took it out into the open air to get a better smell.” They also took samples back to the Silver Dollar and tried them in cocktails.