While airlines seem to be coming up with tighter and tighter seats in economy class, business and first class markets are still seeing many carriers striving to offer the most attractive seating options, especially on lucrative international routes.

United Airlines has been one of the last major carriers in the U.S. to install flat-bed or even “lie-flat” seats on many of their planes. Their international 747s and 767s have been converted for some time, with business class seats that recline 180 degrees.

But passengers on international 777s have been dealing with the old-style business seats, which are a big step down, for example, from British Airways’ flat-bed seats, or even Lufthansa’s lie-flat angled seats.

Now, the 777s, over a third of United’s international fleet, are finally being converted. Three are done now, apparently nine will be done by the end of the year, and the rest in 2011.

The results, mostly good, but there are some caveats — there will be some unhappy people.

For starters, the new business class will have only 40 seats, down from 49. In effect, that is nine less seats for upgrades. These upgrades have already been getting tougher, as countless posts and articles will attest. Limiting the possibility of upgrades may have other repercussions.

The new configuration is also eight across instead of seven. Personally, I love the flat beds, but I am not a very wide person. However, large or broad-shouldered travelers may find it an issue.

The new business class seats also have a touch-screen on-demand video and audio system. No complaints there at all, except less technologically savvy travelers may have to ask flight attendants for help.

In addition, some of the seats face backwards. In general, except for takeoff and landing. Personally, I don’t find the difference noticable in flight, but I have changed seats twice in the past year on the request of fellow travelers who were “flying backwards” and didn’t feel comfortable.

And row 10, the last row of business does face backwards, right into coach, with a transparent curtain. Not an ideal situation, though when I mentioned this to flight attendants I was told they have all been suggesting that the airline change future planes to have that back row face forward.

There are also changes in economy class. The new seats are supposed to be more comfortable, with what will feel like more recline because of the design.

The seats also have individual touch screen entertainment, with nine free movie choices, and extra “premium” entertainment for about $10 a flight.

Plus, the configuration is different, which will no doubt occasion some grouchy letters. Instead of 2-5-2, the seats are arranged 3-3-3.

Personally, I prefer the new design, because it eliminates that dreaded middle seat of five. But travelers who have been lucky enough to book two together on the side in the past will be disappointed.

On the other hand, as a travel agent, I can report that most of the time those paired seats have been gone four to six months in advance during vacation times. Except in the premium Economy Plus section.

Anyone who pays Economy Plus with the new planes will have the option of paying for a window and aisle, and hoping no one buys the middle between them. (Presumably those will be the last to sell.)

One other thing, because there are so few of these newly redone planes, passengers may not know they are booked on one until the last minute.

In fact, in my case, I had a waitlisted upgrade clear just a few days before the flight, had booked a seat assignment, and found it had changed the night before when I checked in online.

Which means however you feel about the new seat arrangement, it’s another reason for travelers booked on United’s 777s both to keep an eye on their reservation, and to check in online, as United may or may not send a message about seat changes.

On my flight there was a fair amount of commotion with passengers trying to switch seats. Which may improve as United is able to assign the redone planes further in advance. In the meantime, for minimal stress, if seat assignments matter, it’s easier to try to fix any problems before boarding.