FORTUNE — When you’re embroiled in an office rivalry, it can seem as though any chance of peace is out of the question. And as time goes on, the rift typically grows deeper. Discord distorts the relationship and emotions cloud its origin. But if we stop for a minute to consider the potential threat that office rivals present and the inherent benefits of having allies, it becomes apparent that burying the hatchet is a worthy pursuit, if not an imperative.
“Positive relationships build political capital,” says Marie G. McIntyre, author of Secrets to Winning at Office Politics: How to Achieve Your Goals and Increase Your Influence at Work. “The more positive relationships you have, typically the more leverage you have in the organization.”
The other side of the coin is that having enemies comes at a huge cost. “It’s just a waste of energy that could be better used for something else,” says McIntyre. “The amount of energy you will spend managing negative interpersonal relationships is a distraction from achieving your work and career goals.”
Put simply, adversaries can bring you down. “The more rivals you have in the workplace, the more you have a chance of being undermined and being ruined in some instances,” says Seth Freeman, professor of negotiation and conflict management at NYU and Columbia.
You may have your doubts about whether making nice with a heated rival is realistic. However, Freeman suggests the power of open communication and good listening is real. Consider the motto of the New York Police Department’s Hostage Negotiation Team: Talk to me. “If [they] can convince someone with a gun to the head of a child to reach a peaceful resolution, there may be more hope than you first think.”
1. Know your enemy
Enemies come in different shapes and sizes, so take a minute to think about your conflict before trying to extend the olive branch. This will help determine the best approach and whether a peace accord is worth pursuing at all. To that end, McIntyre puts adversaries in three categories: focused, emotional, and vengeful.
Focused adversaries are people who are trying to accomplish a certain goal you stand in the way of — a promotion, assignment, or responsibility. With these folks, it’s nothing personal. “If you’re trying to convert a focused adversary, it’s a matter of convincing them that one, you’re not in their way, and two, that they are more likely to succeed in achieving their goals by being cooperative with you,” says McIntyre.
Emotional adversaries are what they sound like — people driven by their own emotional needs. “You can usually tell an emotional adversary because they’re difficult for lots of people — not just you,” says McIntyre. These people tend to be overly critical or even downright angry. The key is not to let them push your emotional buttons, says McIntyre. “You stay in that pleasant, professional, cooperative mindset –even when they’re not being very pleasant back.” In these cases your best bet is to tolerate and neutralize them rather than worry about converting them to allies.
Vengeful adversaries are people who are out to get you, says McIntyre. “They’re mad at you and they’re out for revenge for something you did,” whether or not you know what that was. Only once you know what their beef is can you begin to reconcile.
2. Watch what you say
When initiating peace talks with an office rival, it’s important to keep it unemotional. Carefully choosing your words and properly framing the conversation can play a big part in that. Use observations and statements of fact, says McIntyre, rather than judgments about personality or work habits. “Make your statements factual, not emotional, so you’re saying things like, ‘The last three times I needed some info from your department … it was very difficult for me to get it.’ Saying, ‘You’re always late giving everybody information,’ is a very value driven statement.”
Framing the conversation with the right tone and language can also help your case. “You don’t have to be a wuss,” says Freeman, “Quite the opposite — but you can say it in a way that’s attractive and winsome.” Freeman also suggests avoiding what he calls “irritators,” which could trigger an argument. “Irritators are expressions that people use that they think are persuasive but actually aren’t. For example, saying something like, ‘I’m making you a very fair offer.’ That kind of statement is more likely to cause someone to be defensive since it’s so blatantly self-serving.”
So as not to reopen old wounds, it’s best not to bring up the past. Stay focused on the future. And describing the situation from your point of view using “I” statements can also be helpful. “This is a semantic trick,” says McIntyre, “but it’s amazing how you can neutralize a conversation or keep people from getting defensive by just removing as many “you’s” as possible.”
3. Find common ground
Perhaps the most powerful way to win over an adversary is to appeal to a common interest. “This is the stuff that has changed the course of history,” says Freeman. “Who would have thought that Stalin and Roosevelt could have worked together? But with a common enemy — Hitler — they were able to successfully form an alliance.”
By putting forward a compelling argument that shows how working together would be advantageous to both parties, you have a real shot at building an alliance. For example, pulling together for the sake of getting a bigger budget for your department is a mutual benefit. Or a common interest that almost any two colleagues can agree on is looking good in front of the boss. Finding common ground is crucial.
4. Warm up to conflict
For some of us, conflict is no problem. We have an issue and we confront it. Yet others shrivel at the thought of such an encounter. If you fall into the latter group, it’s time to start working on it, says Jim Waldroop, co-author of The 12 Bad Habits That Hold Good People Back: Overcoming the Behavior Patterns That Keep You From Getting Ahead. “If you know that conflict really makes you anxious, the time to start dealing with it is not when you’ve got something important on the line. What you want to do is start in other arenas so you can basically build up your strength.”
Waldroop suggests warming up to conflict where the stakes are lower, which is likely outside your work life. For example, something that you might just let go, like if your dry cleaner tears one of your shirts. “Don’t just let it go,” says Waldroop. “Go and practice your conflict skills by confronting your dry cleaner.”
In the end, it’s important to have realistic expectations. Try to convert enemies into neutral parties first rather than trying to make a best friend off the bat. “The bottom line is, adversaries are dangerous,” says Waldroop. “They want to do you harm. And if you can make that enemy at least into somebody that is not out to stab you in the back, then you’re better off.”