Certainly women have made inroads in corporate America, but a Pew Research Center survey released Wednesday points at why women struggle to climb to the corporate world’s highest ranks—and often tone down their ideas, hide behind an agreeable facade or leave the workplace altogether.

Four out of 10 surveyed in the Pew study said that there are double standards for women seeking the highest levels of leadership in politics or business. They added that women have to outshine their male counterparts—and more than one-third of respondents believe the electorate and corporate America are not ready to put more women in top leadership positions. (See also: Management lessons from Sony’s gender pay gap.)

That conclusion comes as no surprise to Howard J. Ross, a diversity expert from Silver Spring, Md., who says “men are more likely, on television and elsewhere, to be seen in the workplace. It affects the way men see women and the way women see themselves.”

Ross, who addressed the issue in his recent book, Everyday Bias: Identifying and Navigating Unconscious Judgments in Our Daily Lives, says, “It’s not just men but women too who have ingrained expectations of workplace roles.”

Google’s (GOOG) disclosure last year that it has a 70% male workforce and its public effort to address that “deserves recognition,” says Ross. Google, along with companies like BAE Systems, Exel, Genentech, T. Rowe Price and Roche Diagnostics are among those who are moving to overcome their workplace biases, he said.

Learn more about how other tech companies are trying to increase diversity from Fortune’s video team:

One step some companies are taking when hiring? Stripping resumes of names and other identifying information and assigning numbers, Ross says.

Roche Diagnostics, a subsidiary of pharmaceutical giant Roche Group, is aiming to make its managers more aware of unconscious bias. It held two bias acquaintance sessions with its senior and middle managers in recent months and has plans for a third at its national sales meeting in late January.

“We are trying to ensure that our culture understands how bias exists everywhere, and being aware of it is critical,” says Bridget Boyle, Roche Diagnostics’ vice president of human resources.

In addition to ongoing training to highlight unconscious bias, the company broadened its recruitment and promotion policies in 2013. More than half of its lower level employees were women but their presence began to thin in middle management, Boyle says.

To spark change, the company instituted a mentor policy that has paired 150 sets of employees over 18 months. It’s also strengthening maternity and paternity benefits and assuring diverse slates of candidates for the 750-800 openings it fills each year, Boyle adds.

Royal Bank of Canada started an effort in May 2013 to raise awareness of bias among its 78,000 employees worldwide. Dr. Mahzarin Banaji, a Harvard University social ethics professor who co-authored Blind Spot: The Hidden Biases of Good People, has held sessions for about 1,000 of RBC’s executives to help alert them of their biases.

In addition to these meetings, employees have access to tests developed by Harvard to assess their unconscious biases and apply their personal findings in workshops. These sessions, says Norma Tombari, RBC’s director of global diversity, are continuing in 2015 as part of the company’s “entire talent management decision-making.” The program covers gender, race, disability and LGBT biases.

Despite such concerted efforts, change won’t be sudden, warns Gerard J. Holder, the author of Hidden Bias: How Unconscious Attitudes on Diversity Undermine Organizations and What to do about It. “We didn’t get conditioned overnight,” says Holder, who works with companies to help reeducate employees on their learned behaviors. “It’s a learning process that has to be done over a period of time, not a training that can be done in three hours.”

A transformed workforce may be a while away, but the Pew study did reveal several gems that hint at progress. Women won high rankings on key leadership traits like ambition and decisiveness. The respondents also said that women place more importance on intelligence and honesty than men do—and that those are essential leadership traits.