Q. Our 9-month-old son is almost obnoxiously healthy: full of energy and ready to play even when I'm dragging at the end of a long day.

He's also been precocious in his development, physically and mentally. He crawled at 5 months, stood at 7 months and is now getting ready to walk. He began to use simple words at 6 months ("mama," "dada," "hot," "ite" for light, "bah" for bath, etc.) and now is fairly conversant with his little one-syllable vocabulary.

Fortunately, I can stay home with him and have enjoyed teaching and playing with such a bright baby. We've never used a playpen; instead, we have allowed him to explore with a few restrictions. For instance, the record player is "no" and he generally respects this, although recently I will hear him tell himself "no-no" while he gets into something he's not supposed to touch. (This is only cute the first time it happens.)

The real problem, however, is that my otherwise adorable child has gradually become a terrible cling-on. We spend all day -- no kidding, we're talking about the whole time we are alone together here -- with David hanging around my legs, whining.

I will play with him for a half-hour or so, giving him my undivided attention, then start the housework. I always tell him, "Mommy has to do . . . whatever it is ," figuring he understands at least a little of what I'm saying. But when I try to run the sweeper (or type this letter), he cries and pulls at my legs. He will play happily, alone, when my sister babysits, but as soon as I walk in the door, we get the same old whining.

My husband bought a baby gate several weeks ago and now our son screams and hangs onto the gate when we use it to keep him in the hallway. He can see most of the apartment from there and keep an eye on me, but if I dare to venture out of his sight he flings himself to the floor, kicking, screaming and crying hysterically.

One day I locked myself in my bedroom so I could have 10 minutes alone. Naturally, he lay outside the door shrieking as if he were being horse-whipped.

What have I done wrong? What do I do about it?

A. Parenthood has such special rewards but not all of them are free. Clinginess is one of the prices you pay.

This is because a young child is so egocentric. Between 8 and 10 months a baby often gets scared when his parents leave the room. If he can't see you, then how can you exist?

That's why your son is devastated when you disappear, not because you've done something wrong. Clinging is just his way to keep you in sight until he's built up his sense of trust -- the main psychological achievement in a baby's critical first year.

You'll have an easier time accepting his new needs if you realize that he'll only act this way for a few months more. After that he'll be so busy getting into trouble that he won't have time to cling.

In the meantime, ask your sister if she'd be kind enough to sit more often. You need some regular breaks.

You'll also find it easier if you change some of your ways at home, since you can't change his.

Let him out of his hallway -- it's really just a big playpen -- and simply take him with you from room to room, chatting with him as you work and letting him push the sweeper a little or stir an empty pot on the floor while you make dinner. He'll cling, but not as much, because he won't feel that you're pushing him away.

While it's polite to tell your child what you're doing, you don't need to get his permission to do your work. He'll always think it's more important to play with him than it is to vacuum the living room, no matter how well you explain it or how many words he knows. And at least some of the time he'll be right.

As you know, every child needs some undivided attention each day, but it needn't last longer than 10 minutes -- which will suit his attention span -- or be given more than four or five times a day, not counting the time you feed, bathe and dress him. By putting limits on these playtimes, you'll find you enjoy them more and so will he, because you'll be more enthusiastic. These are the times when you call him on his toy telephone, blow bubbles together, dance him around in your arms, or kick the old Nerf ball around. So he'll learn that you'll always come back, you might read Dad's Back, a charmer by Jan Ormerod about the father who comes home from work (Lothrop, Lee & Shepard; $4.95), or play peekaboo. These will be treasured playtimes, but they shouldn't be given when he cries for them, since that would just make him inclined to use tears as a lever.

Comfort him when he's unhappy, but sometimes he needs you to do this in a light, kidding way: he whines; you whine back, as if he were joking about it.

Parenthood is a serious business, but you don't always have to take a child as seriously as he takes himself.