FORTUNE — Dear Annie: Your column on how to network without wearing out one’s welcome caught my eye, because I’ve been struggling with the exact kind of “networking fatigue” you mentioned. Thanks to a couple of high-profile positions I’ve held, I’m very visible in my industry, and know a great many people in it, so I receive a constant flood of requests for recommendations (both “live” and online), references, introductions, job leads, advice, and so on.

I want to be helpful, especially to people who have been job hunting for a long time, but this is networking run amok. Do I have an obligation to serve as a reference, even for people whose work I either don’t know that well or don’t think was so great? And can I honor some requests for help and not others without burning any bridges? — Mr. Popularity

Dear MP: To answer your first question first: No. You are under no obligation to give anyone a reference if you would rather not. Legally, past employers aren’t required to respond at all to reference requests, and most big companies have a policy of limiting their (entirely optional) responses to a bare minimum of information, i.e., job title and dates of employment.

But legalities aside, your larger dilemma is how to do the right thing without letting your helpfulness eat up every spare minute of your day.

Marc Cenedella, founder and CEO of executive career site TheLadders.com, has a few thoughts on this since he, like you, is constantly besieged by networking requests. He offers these four suggestions:

1. Set a time limit. “In essence, this is a time management issue like any other, whether it’s how much time you’re able to spend coaching your child’s soccer team or how many hours per week you want to put into volunteer work,” he notes. “The answer could be zero, or 10, or whatever works for you. But decide in advance what you’re willing to commit to, and then stick to that.”

2. Devote the most time and energy to the conversations you enjoy most. To be worth doing at all, networking should be a two-way street. “If you’re also getting something out of helping others, it will keep you from burning out,” Cenedella says. “One aspect of this is, do you enjoy chatting with 10 people for 10 minutes each, or would you rather have fewer, more in-depth discussions? Knowing your own style will help determine your strategy.”

An example from his own experience: As the founder of a successful company, Cenedella says he hears from lots of entrepreneurs looking to pick his brain. To separate the truly serious inquiries from the less so, he usually recommends a book like Founders at Work by venture capitalist Jessica Livingston.

“If someone is willing to read that and get back to me, so we start our discussion on the same page so to speak, then we can have a meaningful exchange of ideas,” Cenedella says. “I’ve found I learn a lot from them.”

3. Foster a discussion that’s independent of you. Here’s one way the Internet can come in handy. “Many times people looking for advice share each others’ questions and concerns,” Cenedella observes. “If you set up a blog or a discussion group on a career site or an online social network, you usually find that people will address helpful comments to each other. You can and should weigh in, of course, but you don’t need to be there all the time.”

4. Don’t angst over it. Although your desire to help people is laudable, if you find that you just can’t respond to all requests within the time limit you’ve set for yourself, “don’t feel guilty,” Cenedella advises. “Everyone knows you’re incredibly busy. It’s why they want your recommendation or your advice in the first place.”

For requests you need to turn down for whatever reason, “create a stock response you can email that says something like, ‘Sorry, but due to time pressures, I can’t honor requests for…,’” he suggests. “There are only so many hours in the day. No one’s going to punish you for that.”

Talkback: Have you been on the receiving end of too many networking or reference requests? How do you deal with it? Leave a comment below.