It's four o'clock in the morning in the back room of the Ben Franklin Post Office.

In predawn solitude, among the gray mail sacks and dingy work tables, Buck Hill plays melancholy blues on his saxophone. His eyes are shut tight, banishing the sight of the bleak mail room and conjuring up his dream of success.

Buck Hill is 53 years old, two years away from early retirement after 20 years as a mailman. He's played jazz sax since he was a teen-ager, made a couple of albums, entertained at the big D.C. jazz clubs in the 1950s -- The Republic Gardens, The Crystal Caverns, The 2011 Club, Boots and Saddle, The Offbeat, Mike's. He still plays local gigs occasionally; maybe he's going to make another album, possibly go on tour.

But he's never made it big. He never dared to make the really big gamble, quit the Post Office, go on the road, try New York, where there were more clubs, contacts that could have led to regular jobs, or tours or record contracts.

"I felt if I went to New York I could play," says the stocky, fine-featured Hill. "But I didn't see how I could do that with a family. I had children to support."

At 5 a.m., after playing for an hour all alone in the Post Office back room, Hill puts the sax back into its black leather case. The other postal workers are arriving, turning on the radio to the rock station they'll play all day. Hill's shift begins.

He sits in front of an enormous bookcase-like contraption divided into hundred of little slots, each one representing a street address in zip code 20005. After sorting 3,000 pieces of mail into their proper little slots, Hill bundles the letters and sets out on his rounds. It takes him until 2:30 in the afternoon to deliver all the mail.

"I used to hate the job," Hill says in his quiet voice. "But I got used to it. It's not like playing the blues, though . . . But I guess going through sorrows helps the music."

In the ballroom of the International Inn the waitrsses are clearing off the dirty dishes remaining from the conventioneers' dinner, a few singing along with the band playing in the corner of the room. Many of these attending left as soon as the last of the long speeches ended. The remaining are gathered around a few round tables. Hill, three other musicians and a singer share the bandstand, and the pay.On a date like this, or on the few nights each month when he plays at One Step Down or Blues Alley or Pigfoot, Buck Hill might take home $50 to $100. When you tell him the waitresses earn more than that, he smiles. "I'm a local and we're talking about jazz," he says.

Hill plays an achingly lovely solo on "Tenderly." A few couples sway around the floor, but most stay at their table, talking, drinking.

One man asks his date to dance.

"I don't like to dance to this," she replies. "Why don't they have disco?"

At 1 a.m. the musicians sit at a corner table, waiting to see if the management expects another set.

"This isn't a listening audience," comments singer Ronnie Wells.

"I close my eyes," says Hill. "I don't even know they're there. But I don't hold back because it's not a club."

"Buck always plays with the same intensity," says Wells. "He plays with the same intensity in his living room."

"Sometimes I wonder why I keep playing," says drummer Donald Bowie. "I tried to quit 10 times in the past 10 years."

Buck Hill flashes his great smile.

Hill should know. During the '60s, the bad years when young people abandoned jazz for rock and the clubs started dying, and Hill made the Post Office a full-time job, he decided to give up the sax. He decided this several times. The longest he could make it stick was six months.

Finally the party ends. The lights go up.

"That's it," says Hill. "I can go home and get some sleep."

In a few hours he must be back at the Ben Franklin Post Office, sorting.

Buck Hill is good. Billy Hart, a drummer who lived near Hill as a teen-ager, who went on to play with the great Stan Getz, who arranged for Hill to make his first record album, recalls telling Hill years and years ago that he was going out to try to make it in the competitive world of big-time jazz.

"I did go out," Hart says. "For some reason Buck has always decided to stay. Due to fate, circumstance and luck, I ended up playing with the greatest of the day. When I was back in town with Stan Getz a few years ago, I went to see Buck. By this time I assumed I would hear the flaws in his playing that I hadn't heard when I was a kid. But I heard him play and he was greater than I even remembered, and I was playing with one of the greatest saxophonists. It's a mysterious thing, but Buck is a true creative genius."

Jeff Lettes, manager of Blues Alley, says of Hill: "I never heard him have a bad day. He's technically perfect. He knows all the tunes. He has a very sweet sound, he's a natural improviser, and he loves it."

But Lettes adds a club such as his can only showcase a local so often. Locals don't bring in the customers.

Hill is home in Laurel, listening through earphones to his second album. The garden apartment is spotless, almost sterile, done in shades of green, the furniture carefully slipcovered. Only an alcove off the living room, dominated by hugh stereo speakers and filled with tapes of Hill's performances, indicates it's a musician's home. He lives there with his wife and the youngest of their three children. Four grandchildren live nearby.

Hill is using earphones, an essential piece of equipment, since his family doesn't quite share his devotion to the music.

"He's not quite satisfied," says Helen, his wife of 32 years, who in contrast to her husband is cheerful and exuberant.

But when Hill's composition, "The Sad Ones," comes on, he closes his eyes and loses himself in the full, haunting sound of the music and afterward acknowledges, with a shy smile, that it is good.

"Where music is concerned, Buck is great," says Post Office colleague Ernest Simms. "It was hard for him to come to the Post Office. This is really a secondary job for him even though he works hard here. Music is first. He's always playing, even on his breaks. But this job puts food on the table and you don't throw that away."

Roger Hill was born in Northeast Washington in 1927. His father was a bookbinder, his mother a housewife and both parents played piano for pleasure. His lifelong nickname came from his early identification with the movie serial hero, Buck Rogers. "And when your first name is Roger . . . " he says with a shrug, indicating the nickname was inevitable.

His brother gave him his first sax, and by age 15 he was so proficient that after practicing in the afternoon, he would go out and jam at local black clubs, music, like most other things, being segregated in those days. His parents never objected to his nocturnal activities, nor did they ask for a break from his constant practicing, taciturnity being perhaps an inherited Hill trait.

Graduation from Armstrong High was followed by the Army -- which he looks back on fondly because he played in the band -- then marriage, kids, and after trying to make a living in the Washington music scene, the Post Office.

He admits it's been frustrating to see musicians who are no better than he is make it: They went out and paid their dues. "But I guess I paid, too. I love it so much. I've tried to quit, but the music calls."

After all the years, Hill thinks he might have a chance to answer that call. His record company, Denmark-based Steeplechase, is talking about a third album and a tour. Hill expects the next record to be more readily available in the States because Steeplechase, which is mostly distributed abroad, plans to open an American office.

Then maybe he will take that early retirement. Maybe he'll even get a manager.

"Music has sometimes brought sadness into the home," says Hill. "My not being successful; it not bringing in money. But I think I'll do well in the end. It will be a little late, but I think I'll do well."