A new study by McKinsey, based on information about 365 CEOs who took office between 1990 and 2010, shows that those who moved quickly to make needed change—in people and in the business—got much better financial results and lasted longer in the CEO role than those who moved more slowly.

These findings certainly line up with my observations as coach and consultant to senior executives: when people in C-Level positions get fired, it’s most often because they haven’t made needed change. As might seem obvious, this is particularly true when the executive has been brought in specifically to improve the business in some significant way. But I’ve also seen it when the executive is taking over as the result of a long-established succession plan. Whenever someone steps into a new senior role, he or she is expected to demonstrate capability quickly—and the most observable path to that is through some marked shift to improve the business.

Before we talk about what this means for the rest of us, understand that “quickly” and “slowly” are relative terms here—in the CEO study, the “fast” CEOs made key people changes within their first year, and major shifts in capital allocations within the first three years (pruning or getting out of existing businesses, or investing in new businesses with growth potential).

It’s important to note that “fast” doesn’t mean “immediate,” because there’s an ironic corollary to this need for speed: another very common reason for C-Level execs to get fired (especially early on) is making major changes too quickly. I’ve watched a number of very talented, smart execs fail over the past few years by attempting significant change before building the necessary political capital and cultural savvy.

And I think this “Goldilocks” rule of change—not too fast or too slow, but just right—is an important guideline for the rest of us to follow, as well. Last week I had the opportunity to engage in brief one-on-one coaching sessions with a number of high-potential mid-level women leaders in the cable industry who had just received, or were about to receive, significant promotions. Without exception I found myself encouraging them to follow this middle path to change:

Get the lay of the land. It’s never wise to attempt change of any magnitude before you know what you’re dealing with. This is especially true if you’re moving to a job in a new organization, but don’t underestimate the importance of this exploration even when you’re just moving up a level in your current organization. Think about it this way: you may be dealing with the same people, but your relationship with almost all of them has changed: peers have become employees; a former boss may have become your peer; those previously senior to you are now at your level. Those changes in relationship can bring many other changes in their wake: there may be information you’re now privy to that you weren’t before, or—conversely—conversations in which you’re no longer included. People may trust you more—or less. For the first few months in a new job, especially, it’s best to spend lots of time listening and observing. Ask curious questions, and really listen to the answers. Don’t assume you already know what people think or what they will tell you.

Build allies. When you do start to make needed change, you’ll want and need support from those around you. The listening I’ve encouraged above will be tremendously helpful in this regard—but it’s not enough. As you begin to understand the situation you find yourself in, notice who is most key to any change: whose opinion matters to others; who can make things happen; who can keep things from happening. Once you’ve figured out who are the key sources of power and influence in your new realm, work to ally yourself with those folks. The most high-integrity way to do this: look to see how you can support their success. For example, if one of your “power figures” is committed to an initiative, how can you help bring it to fruition? If someone with whom you want to ally yourself is encountering a problem, how can you help solve it? It’s simple: when you help others, they will generally be more likely to want to help you.

Show early returns. As you’re figuring out the landscape and building allies, look for a simple change you can make during your first few months that will help the company, be fairly easy to implement, and that you’re reasonably sure most people will see as positive. It’s a great way to demonstrate early on that you’re a person who can make things happen, without using up your nascent political capital or doing anything too risky.

Socialize the changes. Once you have the understanding and the relationships you need in order to plan and implement more significant changes (a department re-structuring, for instance, or a new approach to your department’s work) be sure to ‘market’ the change to your key allies before moving forward. This is especially true for your boss (with whom you should be collaborating closely throughout any big change), but remember the other important decision-makers affected by the change, as well. Let them know what you’re planning, why you think it will help—and ask for their input. Be especially open and curious if they disagree, or don’t see the need for the proposed change: really understanding their hesitation can help you make sure you don’t inadvertently jump off any metaphorical career cliffs. Remember, these are the people whose support you’ll need to make the change work. Use what you hear to modify either the plan itself or how you communicate it. Don’t move forward until you’re pretty sure you’ll have the core support you need.

Just Do It. Finally, once you’ve done all this—pull the trigger. A few years ago, I worked with a senior executive to craft a much-needed re-organization, get support from the CEO (his boss), and put together a feasible plan for implementation….and then I watched as he made excuse after excuse not to move forward. After almost two years of circling the airport, he was let go. Big change is scary, but when you’re sure it will help the organization and you’ve built the support you need—take a deep breath and move past your fear or self-second-guessing. Remember, this is you chance to show what you’re really capable of doing.