So I decided to apply for an opening similar to my old job, and unfortunately I sent an email to the person who replaced my old boss that included an explanation of why I left, that is, why working for this new person’s predecessor was so frustrating. Now, I’ve discovered that both the director of human resources and the new boss were, and are still, so offended by that email that I won’t be considered for any position at the company, despite my qualifications. I really want to go back because, despite the problems, I’ve realized that I was at my happiest when I worked there. Is there any way I can apologize and persuade them to rehire me? — Anonymous, Please

Dear A.P.: Yikes. You may have well and truly burned this bridge right down to the ground. But a lot depends on whether you genuinely regret what you put in that disastrous email.

“People have pretty good B.S. detectors, and they can usually tell whether you’re sincerely sorry,” says Gregg Ward, CEO of San-Diego-based executive coaching firm The Gregg Ward Group, whose clients include Bristol-Myers Squibb, Lockheed Martin, and NASA. Ward is also the author of a new book, The Respectful Leader: Seven Ways to Influence Without Intimidation. “If you’re only apologizing in order to get what you want — in this instance, to get rehired — don’t even bother. Just move on.”

But let’s suppose you really are sorry about having given in to what Dorothy Parker used to call “a bad case of the frankies.” Apologies in workplace settings are especially tricky, and CEOs in particular are notoriously bad at them. Public figures often hide behind “a non-apology apology,” says Ward. “We’ve all heard politicians, movie stars, and athletes make non-apology apologies after they’ve screwed up somehow and put their careers at risk.” The hallmarks of these phony mea culpas are “weasel words, such as, ‘I’m sorry if what I said was hurtful’ or ‘I’m sorry to anyone I might have offended,’” he adds. “All of these phrases shift responsibility away from the apologizer, so nobody believes he or she really means it.”

You definitely want to avoid that, and make a real apology, which by Ward’s definition includes no fewer than 7 parts. (Plenty of academic research backs him up on this, by the way, including one recent Ohio State University study that found that, among the half-dozen steps it takes to win someone’s forgiveness, “accepting responsibility” is the single most important element.)

Here are the 7 steps:

1. Admit you were at fault. It’s tempting to try shifting the blame to other people — or the weather, or the traffic, or Jupiter in retrograde — for our own mistakes. Don’t. Simply acknowledge that you shouldn’t have written that email, period.
2. Describe why what you did was wrong. Pinpointing exactly what was unkind or unprofessional (or both) about your email could help persuade the people offended by it that you understand, and value, their point of view.
3. Skip the excuses. This one is so crucial that it’s essentially a reiteration of Number One, above. Maybe you were having a rotten day, or your parakeet had just died, or (most likely) you had been frustrated with your old boss for so long that you just needed to vent. But here’s the thing: The people whose pardon you’re seeking do not care. “As soon as you make an excuse,” says Ward, “the other person shuts down.”
4. State that you’re truly sorry. Swallowing a big gulp of humble pie is painful for many of us, Ward notes, because “we don’t like feeling guilty, especially when we really didn’t intend any harm. It’s a blow to our self-esteem.”
5. Promise it will never happen again. To avoid creating the impression that you’re only apologizing in order to get rehired, “you have to make it crystal clear that you will never make this mistake again no matter where you work in the future,” says Ward. “It’s not about getting a job. It’s about learning from your mistakes and becoming a better person.”
6. Offer to make amends. If you can think of any way to make it up to the people you offended, suggest it. Since you don’t work at the same company (yet) as the recipients of your apology, here’s where you could say that you’re hoping they’ll give you a second chance to prove yourself.
7. Act on #6. If possible, demonstrate you mean it by following through.

“People do forgive you if you take all seven steps, and often they respect you even more” than they did before you messed up, Ward says. But getting there isn’t easy — particularly in your case, he adds, because “you have to apologize, separately, to each of the two people who are upset with you.”

The encouraging part, of course, is that your willingness to repeat this process twice just might convince both the HR chief and the new boss that you’re sincere.

Good luck!