In 1908 Roald Amundsen of Norway planned an expedition to the North Pole. He got scientists to share their equipment, won a grant from the Norwegian Parliament and persuaded many to pour money into the project. He borrowed a schooner called Fram and recruited men willing to risk their lives on a journey through the Bering Strait. Ordinary Norwegians cheered Amundsen on, imagining he would plant their flag in a land where no one had ever been. Then Amundsen got word that the Americans Robert Peary and Frederick Cook had beaten him to the North Pole. Now what?

Amundsen’s quandary is all too familiar to entrepreneurs. Launching an ambitious endeavor requires enormous support. You need to attract funding, staff and media coverage. And you need a good story, told with passion and conviction. With any luck, enthusiasm builds around the story and investors pile in, along with employees, partners and, eventually, customers. But often innovators realize they’ve made a mistake and that they need to pivot.

Changing direction is, in theory, a good thing for a business. After all, Twitter launched as a podcast directory, and YouTube was once a dating site. But pivots can incur a penalty if they’re not correctly managed. A reorientation is an implicit admission that the plan to which the founders were once committed was flawed. Deviations can suggest a lack of competence, and investors, employees, journalists and customers need to be persuaded to stick around.

In recent years we’ve interviewed hundreds of founders, corporate innovation chiefs, market analysts and financial journalists, and reviewed dozens of news releases, analyst reports and media stories. From this research we’ve identified a sequence of stratagems that are critical to establishing and maintaining stakeholder support during major reboots.

The Pitch: Focus on the Big Picture

To build early credibility entrepreneurs must have a unique, concrete plan that meets a specific market need. Yet in their eagerness to gain initial support for their solutions, they can box themselves into a corner: The more specific a startup’s narrative is, the more likely it is to turn out to be wrong. To avoid this trap, our research shows, savvy entrepreneurs craft broad narratives — umbrella ambitions rather than narrow solutions — that leave room to maneuver along the way.

The use of big, abstract ideas encourages audiences to see what they want to see — in much the same way voters respond positively to candidates who take ambiguous positions on issues and thus leave their stance open to different interpretations. Our research indicates that entrepreneurs who follow a similar approach with stakeholders generate more support and, ultimately, get higher valuations.

Consider the early days of Netflix. Reed Hastings, the company’s founder, anticipating a later switch to streaming video, started with the stated purpose of offering the best home video viewing for everyone — not DVDs by mail, which was the company’s original product. As the business pivoted to digital distribution, the original sweeping ambition still made sense.

The Pivot: Signal Continuity

The human mind values consistency. Audiences are thrown by a confusing plot; they view inconsistent organizations as less legitimate and ultimately less deserving of their support. But people are less likely to register deviations as significant if these seem to be in line with larger aims.

When Steph Korey and Jen Rubio, the co-founders of the luggage startup Away, realized that their first suitcases would never be ready for Christmas as they had promised, they threw themselves into making a coffee-table book about travel instead. Though it came with a gift card redeemable for a bag the following year, the move could have easily unnerved supporters. Yet the founders maintained credibility and support by spelling out how the move fit with their higher-level goal of building a travel and lifestyle brand. While luggage was a key part of that brand, a book worked, too. Investors were convinced, and so were journalists. Within a few weeks 2,000 books had been sold (meaning 2,000 bags had been pre-ordered).

The Aftermath: Move Quickly But With Humility

Swift retreats don’t always sit well with customers and other stakeholders, who may feel abandoned after a reboot. Empathy and remorse are a balm when informing people of changes they may not welcome. But too often entrepreneurs think empathy is a sign of weakness. Some simply make the change and never admit they were wrong. Instead of preparing audiences for a change, they spring it on them. Only when stakeholders react do they apologize. By then it’s too late.

In 2012, Glitch was a struggling online video game that centered on collaboration. Its founders soon realized that the messaging technology developed so that gamers could communicate with one another would make a terrific tool for companies, so they transitioned to that more promising business. Glitch’s creators showed humility and remorse for how others would be affected. The company issued a public apology, saying that the game had failed to attract enough players. Executives empathized with those who had signed up and thanked them for their support. They gave them useful information about the shutdown, such as refund details. The message to stakeholders was honest, helpful and sensitive to their needs. In short, it was kind. In the end, Glitch’s pivot didn’t provoke a serious backlash and the new business, the hugely successful communication platform Slack, launched with roughly $17 million in funding from Accel Partners and Andreessen Horowitz, both original Glitch investors.

WHILE OUR RESEARCH has focused on startups, the same principles should apply when big companies pivot to new business models. Think of how much easier it has been for Marc Benioff at Salesforce to move into new business lines given his firm’s broad aim of “democratizing digital transformation.” Or the plaudits given to Microsoft after its leaders justified its shift to cloud-based services in 2013 by linking the change in strategy to the company’s broad vision of “modernizing the workspace.”

Great leaders understand that stories and sense-making are especially important during periods of uncertainty. As the COVID-19 pandemic upends industries and changes consumer behavior, businesses will increasingly face the need for strategic reorientation. How they explain their reinventions will play an outsize role in their ability to endure. Amundsen recognized this. Upon hearing that others had beaten him to the North Pole, he decided to change course — literally. It wasn’t the route or the destination that mattered, he told his fellow Norwegians. From the beginning, his was a mission of scientific discovery. And he had stayed true to that aim. Amundsen went on to become the first person ever to reach the South Pole.