AS THE SUN sank in the west, my star continued to rise. For the third time in one week, a small assemblage of sophisticated people gazed upon me with avid interest and utter attention. I now have to admit that the key to social success is available to almost anybody. All you do is announce you've just made an overnight trip via Amtrak sleeper.

"You slept in a compartment on a train?" said one wide-eyed woman. "I didn't know you could do that in this country."

"Well, you look all right," said a man who is not easily one-upped. "All you read about are crashes and derailment."

"But surely you didn't sleep?" said another headline reader. "Aren't the roadbeds too rough? Didn't I just hear something about how Amtrak isn't succeeding because the railroad companies are not maintaining the tracks?"

As you may have noticed, in some gatherings it's easier to get the limelight than keep it. However, I have not watched "Meet the Press" for nothing. The trick is to ignore all questions to which you don't know the answers and say whatever you came there to say anyhow. I side-stepped the matter of maintaining the tracks and got straight on with the really important stuff -- my firsthand experience.

I explained how Amtrak selects its customers. You may think it's the other way around, but that's not necessarily so. I, at least managed several times to call when Amtrak's computer was "down" and consequently was several times rejected; Amtrak's humans told me the sleepers were full. I called back, though, and eventually persistence paid off. The computer got "up" and apparently liked me. I had my choice of accommodations.

The variety was interesting. Amtrak seems to be one of the few innkeepers to give single travelers a break, but let me preface that.

All Amtrak long-distance trains that run overnight normally have sleeping cars attached, most with roomettes and bedrooms. On five -- Montrealer, Lake Shore Limited, Night Owl, Broadway Limited and Silver Meteor -- there are also "slumbercoaches." Roomettes and slumbercoaches are usually for one person, although there are double slumbercoaches, and you allegedly can squeeze one child and one adult into a roomette. Bedrooms are bigger, but two adults and two children, preferably small, are the limit.

The new Superliner on Amtrak's Empire Builder between Chicago and Seattle is a preview of coming attractions: family bedrooms (up to four people), special bedrooms (equipped for the handicapped) and one- and two-person economy and deluxe bedrooms.

All units except the economy and family bedrooms have private wash basins and toilets; the exceptions use communal facilities. Each also has adjustable air conditioning and a full window. For lone travelers, though, the equally important news is that single accommodations cost about one-third to one-half less than doubles.

Given the choice, I'd always take a slumbercoach over a roomette. For one thing, there's the cost. Examples: $16.50 a night single compared to $39.50 New York-Montreal, $24 vs. $71 New York-St. Petersburg, plus coach fare, of course. Secondly, you don't have to fold up the fold-down bed if you want to use the toilet. The bed itself measures 74 by 24 inches and has a partial guard rail to make sure you stay tucked in. With the bed folded away, you're sitting in an enclosed space that measures about 4-by-4-by-6-feet high. Across from your seat is a steel "door" that makes the whole unit look like an antechamber to one of those morgue slots where they refrigerate unclaimed bodies, but never mind; the thing feels oddly cozy.

Once installed, I wandered down to the roomette-bedroom car to look at what I was missing. The porter agreed with me: One person misses nothing. For longer than overnight, roomettes might be preferable, but I'm not convinced. They are, though, slightly larger and upholstered.

My train had only a snack bar, no diner. That meant sandwiches, soft drinks, beer, wine, liquor miniatures and junk foods. If I had boarded hungry, I wouldn't have been thrilled. But I had earlier collected a free timetable, knew what to expect and planned accordingly. I was going from Washington, D.C., to Boston. Instead of just taking my night train (which left a little after 10 p.m.), I'd found one at 7, rode coach to Baltimore one hour down the line, and then gotten off to have dinner at a nearby restaurant. After a good gorge, I waddled back to the station just in time to catch my sleeper and go to bed. Since there's no charge for stopovers, Amtrak affords some pretty good possibilities for such breaks, though naturally only along routes with frequent service.

But traveling while you sleep is the real bonus, and Amtrak does let you do exactly that on quite a few routes. Between roughly dusk and dawn you can, for example, go between such cities as Washington-Philadelphia-New York and Montreal; Washington and Cincinnati; St. Paul-Minneapolis and Chicago; Pittsburgh and Chicago; Phoenix-Tucson and Los Angeles; Flagstaff (Grand Canyon) and Los Angeles; or one direction New York to Cleveland, Memphis to Chicago, Charleston to New York.

While training the lying-down way may not cost less than flying, the rooling route can turn out to be more economical than it looks at first glance if you would have had to pay for a hotel room on top of your plane ticket. Comfort and convenience? Well, we went city center to city center, arrived only 10 minutes late, experienced no crashes, no derailings, no hijackings. The air conditioning worked perfectly, my slumbercoach was clean, trim and tidy. The roadbed was rocky in spots, but we went so slowly along these parts that I was barely troubled.

Color me lucky? Maybe. I did, though, give myself an edge. I looked for a fixed-up car and knew they had been working on the roadbed. No doubt about it, Amtrak still has its bad days and some poor equipment, plus a few unrealistic passengers who somehow expect something more on the order of a waterbed with wheels.

Most criticism centers on infrequent service, tardiness, heating and air-conditioning systems that malfunction, and lack of speed. While some trains go as fast as 60 mph on the average, others go as slowly as 34.7, and the average system-wide is 48 mph, with late arrivals about a third of the time. And although you aren't guaranteed a heating or air conditioning failure on the San Francisco Zephyr or the Southwest Limited, you'd better be prepared. Those are reportedly the weakest links in the chain. Fortunately, improvements are scheduled on the Zephyr within the next month.

My trip, though, was a three-way winner. I did well in comfort, convenience and price. "Well, why don't they tell people they have all that?" said one of the listeners treated to my success story.

I do believe poor Amtrak tries. Of course, if all of us hear and respond, there goes social stardom. Then only a really miserable trip will get you center stage.