LAS VEGAS — Ben Baldanza, chief executive of Spirit Airlines, does not seek business travelers. Nor does Andrew Levy, president of Allegiant Air.

Though both discount airlines are prospering and adding routes in places where the major airlines have cut back service, Spirit and Allegiant market strictly to budget leisure travelers willing to put up with limited service, lots of added fees and cramped seating to get cheap fares.

“Our seats don’t even recline,” Baldanza said last week at the Boyd Group International Aviation Forecast Summit here.

Well, I snapped to attention hearing that, given the furor about the etiquette of reclining one’s coach seat, and also given the realization that I seem to be now putting up with limited service, lots of fees and cramped seating, though at expensive fares, on the major airlines.

I’m pretty sure Baldanza meant no irony with his comment, despite the growing Internet clamor over an episode a day before on a United Airlines flight from Newark, New Jersey, to Denver. As you may have heard, there was a spat involving a passenger deploying an ingenious $21.95 gadget called the Knee Defender to prevent the passenger in front from reclining her seat into what he regarded as his personal space. Long story short, she is said to have tossed a cup of water at him, whereupon the pilot decided to make an emergency landing in Chicago, with serious inconvenience to the more than 160 other passengers.

The social media flap intensified a few days later after an American Airlines flight from Miami to Paris was diverted to Boston when a man arguing with another passenger about reclining a seat is reported to have grabbed the arm of a flight attendant who tried to intervene. That man was taken off the plane in Boston and charged with interfering with a flight crew.

So the seat-recline wars, heretofore fought mostly in simmering silence, are thrust into the open. On Twitter, one passenger noted that in a packed airplane, “The air between the back of your seat and my face is my air space,” while a flight attendant admonished in a Mashable article: “Toughen up, fliers. There’s no rule against reclining.”

That flight attendant was Heather Poole, the author of an amusing book that I have mentioned here before, “Cruising Attitude: Tales of Crashpads, Crew Drama, and Crazy Passengers at 35,000 Feet.” Poole followed with this reasonable tweet: “I do blame the airlines for squishing the rows so close together. It’s ridiculous. But that doesn’t give anyone the right to act childish.”

Most passengers submit quietly, if not cheerfully, to the indignities and cramped coach seating on packed flights, with only the occasional outburst. But flight attendants say they often need to referee disputes about seat-reclining, and a survey of 1,000 international fliers last October by Skyscanner.com found that 91 percent favored an outright ban on seat reclining, or a setting of specific time periods for reclining, on noninternational flights.

So it would seem that an airline that has nonreclining seats as well as cheap fares might have at least some market appeal for some business travelers, especially those in small and midsize cities where it’s sometimes harder to find a convenient flight. Given cutbacks by major carriers, “We’re very happy to go in where we see a gap in service, which has continued to make small cities into bigger and better opportunities for us,” said Allegiant’s Levy, who nevertheless insisted that the airline’s strategy was entirely focused on budget-minded leisure travelers.

Neither Spirit nor Allegiant professes any interest in claiming even a small segment of the business travel market. Nor, given limited route networks and frequencies, has that market shown any measurable interest in them. In fact, Allegiant, while stressing that my business would of course be welcome, went to some length to tell me why the airline didn’t really advertise to business travelers. “Beyond not marketing to business travelers, we don’t even do any connections,” said Jessica Wheeler, an Allegiant spokeswoman.

Spirit takes a similar modest attitude about itself. “Doesn’t everybody really hate flying Spirit?” Baldanza joked at the airline conference, alluding to familiar complaints in some quarters about Spirit, including its placement at last, 11th out of 11 airlines, in a ranking last year by Consumer Reports. But, he added, “We know that some people get us and some don’t get us.”

I have occasionally looked for a Spirit or Allegiant option when booking a flight — but only on those occasions where my timing was flexible and my curiosity was sufficient to brave the unknown. Still, in this personal-space battle, I’m with the side that says airlines should prevent coach seats from reclining altogether.

While neither Spirit nor Allegiant publicly expresses interest in business travelers, maybe there’s a trend in the air. Ryanair, the giant cheap-fare, no-frills airline that helped revolutionize budget leisure travel in Europe, seems to have gotten the idea.

Having discovered that 25 percent of its passengers are in fact on business trips, most of them younger fliers willing to rough it for a cheap fare, Ryanair wants a bigger share. Last week, Ryanair announced a “Business Plus” service, at higher but still discounted fares, featuring priority boarding, fast-track airport security passage and premium seats aimed at business travelers.

And no, the seats on Ryanair don’t recline either.