NEW YORK — The place: Feinstein’s at the Regency, the largest of New York’s three jacket-and-tie niteries. Early in June, recording star Michael Feinstein and Broadway leading man Cheyenne Jackson sang “I have dreamed that your arms are lovely” — to each other — while audiences dined on crispy oysters with lemon bourbon mayonnaise, sweet potato fries and rosemary-spiced macaroni and cheese.It wasn’t standard fare, either on stage or plate, at this celebrated Park Avenue venue. But with the economic situation continuing to pinch pocketbooks, new directions seem warranted on this top-dollar circuit. Feinstein’s has made the most radical changes. “People will always want to go out to eat and listen to music,” says Regency director of entertainment John Iachetti. The trick, he adds, “is to get new people in to see the club.” Feinstein bookings play a five-night week, usually with double-headers on Friday and Saturday. The room has occasionally presented non-nitery names on dark nights, with a reduced cover charge and minimum ($40 plus $25; corresponding figures for big-name acts are $95 plus $40, with “premium up-front” seats topping out at $250). Some of these one-and-two-nighters have done spectacularly well, including Jackson — whose jam-packed houses in March led to the June engagement with Feinstein — as well as musical comedy regulars like Sutton Foster and John Tartaglia. Hence a new policy. This year, the room will, for the first time, operate through the summer, moving from 200-odd nights a year to more than 300. With lower tariffs and no competition from the vacationing Cafe Carlyle and Oak Room, Iachetti expects the summer series to bring in new customers. (Proprietor Jonathan Tisch is wholly behind the expanded schedule, so much so that he approved a $100,000 expenditure for a new lighting system.) Acts run the gamut from Clayton Bryant, Davis Gaines and Dave Frishberg to the likes of Renee Taylor and Joe Bologna. Those oysters and fries come courtesy of celebrity chef Alexander Smalls, a proponent of Southern revival cooking from the fondly remembered Flatiron-district haunt Cafe Beulah. Supplementing the established menu with tastes from visiting chefs is yet another step toward bringing in a non-East Side crowd — and hopefully turning them into repeat customers. The fabled Oak Room at the Algonquin Hotel, now entering its 30th season, has also been looking at ways to combat belt-tightening. Noticing that phone reservationists were fielding more and more questions about the menu, entertainment director Barbara McGurn has reduced the prix fixe tariff; with a smaller differential between the minimum and the prices, dinner business has actually expanded. The Algonquin concentrates on dedicated cabaret singers as opposed to stage or film celebrities looking for a New York gig; annual visitors Karen Akers, Andrea Marcovicci and KT Sullivan take up more than a third of the 40-week season, cultivating a base of repeat customers. The Algonquin is the only room where the star regularly greets fans in the lobby after each perf. The economic crunch is less apparent at the Carlyle, per entertainment director Peter Gallagher. “We are lucky to find ourselves in very fine shape, due to the nature of the room and the artists,” he says. Prices are high; when Judy Collins returns in September, customers will pay a $125 cover charge before even contemplating the menu. “We like to joke that we cost less than going to a Yankees game,” Gallagher says. Such acts as Elaine Stritch (who lives upstairs in the hotel), Collins and the husband-and-wife team of guitar-wizard John Pizzarelli and Jessica Molaskey attract repeat trade, keeping the intimate, Vertes-decorated jewel box warm and cozy. Even so, Barbara Cook — one of the Carlyle’s top attractions of recent years — recently switched her New York base to Feinstein’s. With a capacity of 140 (compared to the Carlyle’s 85), the Park Avenue room is able to guarantee a bigger take. As for Feinstein and Jackson, business was so brisk for the nine scheduled performances of their dazzlingly entertaining joint act that they returned recently for an additional six shows. That engagement brought in even more first-time visitors, who seem likely to return to Feinstein’s at the Regency next season for similar fare.