This could be you.

FORTUNE — Dear Annie: I work at the headquarters of a Fortune 500 company in a major city. The suburb where I live is not that far away as the crow flies, but the horrendous traffic (even in the predawn hours) means my commute often takes more than an hour each way, and it is a huge drain on my energy. Then, when I get to work, my day is so full of stupid little interruptions that it’s hard to focus on one thing long enough to finish it.

For both of these reasons, I would be a lot more productive if I worked from home at least a couple of days a week — no commute, no distractions. The problem is my boss. When I have approached him about this, he always says, “If I can’t see you, how do I know you’re working?” He says it jokingly, but actually I think he means it. Also, he has brought up the fact that Yahoo YHOO , Best Buy BBY , and HP HPQ have limited or banned telecommuting, and expressed concerns about data security if people are working from home. Any ideas about how to persuade him to let us try it anyway? — Roadblocked

Dear Roadblocked: Next time your boss brings up Yahoo, Best Buy, and HP as paragons of policy, says David Heinemeier Hansson, you might point out that “all three are in trouble, so they need all hands on deck. Why would any company want to join that club?”

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Far more relevant is that telework has quietly become the rule, rather than the exception. According to a survey this past July by HR trade group WorldatWork, 88% of U.S. companies now allow or encourage telecommuting. Some, like IBM ibm , insist that most of their people work remotely most of the time. In a new book, Remote: Office Not Required, Hansson cites a white paper from Big Blue that estimates telecommuting has saved the company more than $100 million in real estate costs.

Remote is packed with other compelling reasons for telecommuting’s rise. Cutting out commutes is better for the ozone layer than having millions of people sitting in traffic jams, spewing carbon monoxide, for hours on end. It allows companies to source top talent from anywhere in the country or the world, without regard for how much face time they can put in at the office.

Working from home or on the road, at least some of the time, also tends to make people more productive. Hansson agrees with you that “the modern office has become an interruption factory, and interruptions are not free. There is a cost in productivity to constantly demanding people’s attention immediately for little things that are not really urgent,” he says. “People who can’t concentrate for more than a few minutes at a time are almost certainly not doing their best work.”

Hansson offers three suggestions for winning over your reluctant boss. First, the idea that you’d be able to get more work done, and do it better, without distractions (and without the wearying commute) makes a good starting point for the discussion. “Don’t frame it as a request for a perk, as if this is a favor you’re asking the company to do for you,” Hansson says. “Instead, emphasize how much better it will be for the team and the company if you are able to work without interruptions. Having you at your most productive benefits the boss at least as much as it benefits you.”

Second, “you’ll need to address his concern about data security,” Hansson notes. “But data is not necessarily secure just because people are working in an office together. Employees take laptops home, they carry company data in their personal smartphones, they go on business trips. If there are security gaps the company needs to address, that is a serious issue whether you are working at home or not.” Before bringing up telecommuting with your boss again, ask your in-house techies for help in hack-proofing the devices you plan to use.

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And third, Hansson suggests enlisting more of your colleagues to the cause. “Trying out telecommuting with just one or two people is doomed to fail, because that one person, or two people, will become too isolated from the group,” he says. “A better way is to have all the people on your team work remotely some of the time, so everyone gets a taste of it, and no one is the ‘odd man out’ who’s always calling in on the conference line at meetings.” At some companies, he adds, teams or departments start with “work-at-home Wednesdays,” so everyone gets at least one distraction-free day per week.

The hardest argument to counter is, “If I can’t see you, how do I know you’re working?” Says Hansson, “It reflects a deep-seated fear of losing control. Fighting that requires that you go slowly and start small — ‘I worked from home on Tuesday and look at all the great stuff I got done’ — and then gradually increase the amount of time you telecommute.”

Hansson says that at his company, Chicago-based collaboration software maker 37signals, where most of the staff works remotely, “the biggest problem we have had is not people goofing off while working at home, but people overworking. They get into a state of flow and just keep going. Sometimes, to keep them from eventually burning out, you have to protect employees from themselves and insist that they take some time off.” But of course, your boss may have to see that to believe it.

Talkback: Have you ever convinced a skeptical boss to allow telecommuting? How did you do it? Leave a comment below.