A new study suggests that CEOs whose cultural values match those of their staffs’ can struggle. That’s not license to be a contrarian, but an opportunity to think about what’s missing.

You’re about to be hired as CEO by an organization that’s excited about a lot of things you offer: your experience, your understanding of strategy, your wisdom about the industry, your poise as a public speaker. Plus, the head of the search committee has told you that you’re a great fit with the culture of the staff.

Don’t get too comfortable.

A good “cultural fit” can be important, but walking in lockstep with the staff’s culture has its downsides. According to a recent report in the Journal of Applied Psychology, it’s not always in the best interest of the CEO to adhere to the culture of the organization that he or she leads. If, for instance, a company takes pride in its get-it-done-on-time environment, a get-it-done-on-time taskmaster isn’t necessarily going to be a boon to the organization. Indeed, it can sow resentment among the staff (“Why’s she lecturing us on what we already know?”). And it can blind the organization to new ways of thinking that don’t stoke new ideas. (What if, in the insistence on hitting all those deadlines, people aren’t thinking about which deadlines take priority, or quality control during the process?)

Put more bluntly, a CEO in total agreement with staff can be overbearing. As the report puts it: “CEOs are least effective when high levels of task or relational behaviors are accompanied by high levels of corresponding culture values. This pattern of relationships suggests that organizational culture can be a substitute for leadership. Because culture provides employees with relational- and task-oriented cues about how to behave, these values and norms can attenuate the need for corresponding leadership behaviors.”

Chad Hartnell, an assistant professor at Georgia State University and one of the study’s authors, suggests that execs would do well to zig a little when their staff is zagging. “Similarities between leadership and culture can produce a myopic focus on things that have worked in the past while precluding employees from acquiring other resources or processes that could enhance success,” Hartnell says in a release from GSU. “CEOs should be mindful about focusing employees on important outcomes and processes that cultural signals may overlook.”

As an example, Hartnell points to former Delta Airlines CEO Richard Anderson, who brought a bottom-line emphasis to a company that complemented its relationship-oriented culture. He pioneered an era of airline mergers, including a successful one with Northwest, that might not have worked in a safer, more change-averse environment.

A few caveats here. First, the study focuses exclusively on CEOs of technology companies, and very few of the CEOs studied were founders, which makes a difference—people building an organization from the ground up are “formative in imprinting the organization’s values, beliefs, and assumptions.” the authors write.

Perhaps more importantly, the study isn’t giving permission to CEOs not to listen to their staffs or try to bully their own cultural vision onto an organization. “CEOs need to be aware of the organization’s culture and adjust their leadership styles accordingly, particularly because it is easier to change one’s leadership behavior than to change an organization’s culture,” they write.

In doing that, the study suggests, leaders should be looking for areas in need of repair. If staff cohesion is a problem, a CEO with a strong relationship mindset can help; if performance is the issue, a CEO who can keep teams on task has value.

“Leaders must search diligently for what isn’t currently being handled by the culture and fill in the gap,” Hartnell says. “They should adopt a leadership style that builds upon the positive aspects of the existing culture, contributing to the culture without undermining it.”

This article was originally sourced from Associations Now and was written by Mark Athitakis.