Julian Lennon closed his eyes and went straight to heaven. The young singer-songwriter’s blissful smile indicated that a vision of paradise was being screened in his mind’s eye.

It turned out that his heaven wasn’t exotic or luxurious. He was just dreaming about enjoying a few weeks off, with no recording studios, no concert halls, no record executives, no nosy interviewers--just leisure.

“Sheer, pure heaven,” gushed Lennon, the 23-year-old son of John, the late Beatle. “I’d do nothing but relax. I wouldn’t even have to go anywhere special. This heaven is very simple. You’d have to go through what I’ve been through to appreciate this kind of heaven.”

He gazed blankly around the living room of the ritzy bungalow of a West Hollywood hotel. “All this is OK, but I’d rather be transported to some place where I could rest and tune out the world.”

For the last few months, Lennon has been working at a furious pace, scrambling to finish his second album, “The Secret Value of Daydreaming.” These few weeks of promoting it precede preparation for a six-month world tour. Rehearsals begin soon.

“I hate to think about it,” Lennon groaned. “I’m tired. They’re going to have to use match sticks to pry my eyes open. I had a week off just before I started to write and 10 days off at Christmas. But that wasn’t nearly enough, not when you’re working every day.”

Couldn’t he have postponed everything? Did the album have to come out now? Did the tour have to start at the end of April?

“Apparently the booking agent knows what he’s doing and the record company people know what they’re doing,” he replied. “They said all this had to happen now. But I still think it could have waited a few months.

“I can see it all now. I’ll have a nervous breakdown in three weeks and they’ll say, ‘Why are you having a breakdown?'--as if they didn’t know I’ve been working much too hard. When I’m in a rest home, they’ll realize they screwed up.”

Lennon’s debut album, “Valotte,” was released by Atlantic Records in late 1984. With two hit singles--the title song and “Too Late for Goodbyes"--the album sold over a million copies. Everyone was saying how much he looked and sang like his father.

“With this album they won’t be saying I’m trying to copy my father,” he said. “I have a bit of a different sound.”

“The Secret Value of Daydreaming” does explore rock more than his first album, which, joked one reviewer, suffered from terminal mellowness.

Lennon admitted that he had to battle producer Phil Ramone, who also works with Billy Joel, to inject more punch into the new album.

“Phil was trying to make this one like the first album,” Lennon said. “He didn’t want to make it too different. He wanted to keep the gentle songs so I could keep the audience I have. I sang very gently on the last one. We did a lot in that basic acoustic sound.

“But I wanted more rock this time. This album is a cross between me trying to make it more rock and Phil trying to make it more mellow. We compromised. But I wanted to put even more energy, even more rock into it.”

Last year, Lennon’s first as a star, he was too busy with touring and assorted other activities to start the second album early.

“I had a month to write it,” he griped. “When they shipped my equipment to where I was writing, it got lost. When it finally arrived, I just had one week to write the songs before I went into the studio. Whatever came into my head that I liked, I used it. I would have liked more time to play back the songs and reflect on them, but there was just no spare time.

“I wrote the songs so quickly I didn’t check the keys I was singing in. When we recorded a song, the key would be too high or too low for me and I’d be straining when I sang it. This album is a very strained album.”

So far, Lennon noted, the reviews of “The Secret Value of Daydreaming” have been largely positive. An exception, the acidic review by The Times’ Terry Atkinson, unsettled him. Cringing, Lennon recalled it.

“He said the album was like John Lennon singing the Barry Manilow songbook. Then he compared me to Frank Sinatra Jr. He said the album was useless, boring drivel and if you want to be bored, listen to this album.” There was anger in Lennon’s voice as he slowly repeated those lines. But that storm quickly passed.

“I can’t stay mad very long,” he said, smiling. “I get grumpy when I read a bad review. I say, ‘How could he say that about my music?’ Then I forget about it. If I got mad every time somebody wrote something negative about me, I’d be exploding all the time. I’d be burned out just from reading reviews.”

For the most part, Lennon noted proudly, the American press has treated him favorably. “I’m really happy about that,” he said. “I need the support. Most of the rest of the world doesn’t like me.”

Outside of America, only Japan and Australia are big markets for Lennon. Even his home country, England, offers him only mild support.

“In places like England, they think this was all handed to me on a silver platter,” he said. “They say, ‘Why is he bothering with this singing, he’s got plenty of money in the bank?’ But that’s her (stepmother Yoko Ono’s) money. I don’t control it. They don’t realize I worked hard to get where I am and to get what I have. But once some people get an idea in their heads, you can’t pry it loose.”

There was a rumor circulating that Lennon was going to guest-star in some of Yoko Ono’s shows during her American tour, which was recently canceled.

But he denied the rumor: “I had no plans to do that. If she had wanted me to do some shows and I wasn’t doing anything, I might have done some. It depends on what she had in mind. If it was to do some of Dad’s stuff, I would have said no.”

Then another rumor bit the dust. Supposedly he almost never talks to Ono: “I do have contact with her. I’ll call her up and say, ‘Do you want to have a cup of tea, do you want to go for a meal or a movie?’ We keep in touch socially. It’s all social too. But we don’t talk business. We don’t want to spoil things.”

Those around him fear he may be the victim of a lunatic attack, just as his father was. Still, Lennon is not, as many think, a prisoner of security. He’s not the most heavily guarded artist in show business after all.

“I have bodyguards on the road, when I’m in situations where I need crowd control, like at concerts,” he explained. “But otherwise I’m not constantly guarded. I live in a small apartment in London, not some big house with a lot of security. I don’t like too much security. There’s no freedom. I’m a person, not some precious diamond that needs guarding every second.”

Lennon said he harbors no overwhelming fear that he’s going to be attacked: “Nobody has tried anything. I can’t live in fear that somebody will. That’s not really living. My life is complicated enough without having to worry about that all the time.”