Inc.com columnist Alison Green answers questions about workplace and management issues -- everything from how to deal with a micromanaging boss to how to talk to someone on your team about body odor.

A reader asks:

One of the managers I supervise is named Megan; she in turn supervises Sarah, a junior analyst. Sarah is one of the best analysts at our firm, but she's often difficult, arrogant, and condescending. For example, she often criticizes her co-workers' ideas in harsh terms or offers to "fix" their work even if they haven't asked for her help. Megan has been coaching her, and there's been steady improvement.

Unfortunately, that progress seems to have come undone last week. The team regularly meets to pitch different proposals in response to our clients' requests; Megan chooses which option to pursue, and after the plan is fully developed, I approve the final version. At this meeting Sarah offered one idea (Plan A) and another employee proposed a different idea (Plan B). Megan chose Plan B to develop further.

Sarah, however, has continued to vocally advocate for Plan A all week, even after Megan made it clear the decision was final. Megan spoke to her privately, but their conversation devolved into yet another argument about the merits of the two proposals. Things seem to have escalated into a feud where Sarah is waiting to be vindicated, Megan is constantly having to reassert her authority to make final decisions, and the whole team is waiting to see who "wins."

Here's the last wrinkle: I'm convinced that Sarah's criticisms of Plan B are accurate. That plan is competent but unexceptional, while Plan A has the type of creativity/inspiration that we aim for (and market ourselves to clients based on).

I do have a great deal of confidence in Megan. She's excellent with people, and her team has consistently produced good results. Sarah probably has more raw talent, but that's true in many of the analyst/manager teams I supervise, and I've never found it a cause for concern.

But I'm in a Catch-22. If I share my criticisms with Megan and ask for changes, I feel like I'll be validating Sarah's inappropriate behavior, encouraging her to act the same way next time she objects to one of Megan's decisions, and permanently undermining Megan's ability to manage her team. At the same time, I have a responsibility to my clients to give them the best product I can.

As for why Megan picked Plan B over A: The former was professionally put together and thorough, whereas Sarah's needed a lot more polish to go from great concept to great reality. Typically, Megan would have evaluated both plans on their ultimate potential, but I suspect Sarah's confrontational way of making her case made it hard for Megan to get enough distance to be objective.

Green responds:

This is hard. You're right to worry about validating and reinforcing Sarah's behavior, as well as undermining Megan's authority and ability to manage her team.

At the same time, though, personality issues shouldn't determine what work you give a client.

Where I ultimately come down is this: The strongest managers are willing to be wrong, and they're willing to give a fair hearing to viewpoints other than their own, even if those viewpoints come from people they find frustrating. Managers who dig their heels in because they don't want to look wrong end up acting from weakness.

So, assuming you're looking for a way to pick Plan A -- Sarah's plan -- because it's the better plan, while minimizing any undermining of Megan and not increasing the chances that Sarah will repeat this in the future...well, I don't think there's a perfect solution, but I think we can get you fairly close to that outcome.

You could coach Megan to frame the decision this way to Sarah: "I've thought about what you've said, and I think you're making good points. I don't think I'm infallible, and I'm willing to give Plan A a try...but I want to talk to you about some of the reasons I didn't prefer A originally. (Insert feedback here about putting together a professional and polished plan.) Also, I need to be candid with you that the way you've handled this situation this week has been problematic. It's not that I don't want to hear opinions that differ from my own -- I do. But I need you to raise those points calmly and collaboratively. This week at times you seemed to be going on the attack, and that's not how I want this team to function. I also need you to accept that decisions won't always go your way. I will always hear you out, but once I make a decision, I need you on board and moving forward with it, not still debating it."

Of course, Sarah may be sitting there thinking, "But it's because I pushed that you eventually ended up agreeing that I was right." And that's true, so Megan needs to address that head-on: "I'm concerned that the lesson you'll take away from this is that if you push hard enough, you'll be able to change my mind. So I want to be really clear with you that what happened this week can't happen again. Sometimes I'm going to make a different call than you would make, and for us to be able to work together effectively, I need to know that you'll be able to roll with it when that happens. Will you be able to do that in the future?"

Megan should also be transparent with the rest of her team: "I've heard Sarah out and I think her points have value, so we're going to give Plan A a try. I worry that this got framed to y'all as a Megan versus Sarah battle, so I want to make sure it's clear that it wasn't. I value Sarah's viewpoint just like I value all of your viewpoints, and I'm willing to reconsider decisions if someone feels strongly and makes a good case. That said, as I've told Sarah, that process needs to look different than it did here -- we should be collaborating to get to the best solutions, not feuding."

Also! It sounds like Megan might be falling prey to a really common manager trap, where her frustration with Sarah is preventing her from objectively evaluating Sarah's input and ideas. If so, it's important for you to coach her around how to respond more objectively. If Sarah is going to stay on Megan's team, Megan has to assess her work with an open mind -- and that's especially true since the reason you're putting up with Sarah's difficult traits is because of the value she brings.

Want to submit a question of your own? Send it to alison@askamanager.org.