Women face a narrower band of acceptable behavior than men do. Women can be powerful. Women can be likeable. Being both is difficult to do.

Last week, I was in California, the ultimate proving ground for that theory. California is the place, after all, where three well-known women — former Hewlett-Packard CEO Carly Fiorina, former eBay CEO Meg Whitman, and Rep. Nancy Pelosi — have learned that acting tough, while key to playing in big-time politics, typically does not win popularity contests.

Stanford Graduate Business School Professor Deborah Gruenfeld, a social psychologist who has studied power and how it works in organizations, dissected the female leadership conundrum last week at eBay’s global women leaders conference in San Francisco. (I spoke there too; see last Wednesday’s Postcard.) People who are viewed as powerful, Gruenfeld explained, tend to:

– Occupy maximum space.
– Lean back.
– Slow down.
– Use sweeping gestures.

The challenge for women — who still occupy only 14.4% of executive officer positions and 15.7% of board seats at Fortune 500 companies, according to Catalyst — is that guys tend to be better at using such body language. And compared to women, men are more socially accepted when they do. Gruenfeld cited an experiment in which a professor presented his students with stories of two managers, Heidi and Howard, handling the same issues with the identical behavior. The names, Heidi and Howard, were the only difference. The students judged Howard to be equally competent but less selfish and more worthy of hiring. (Facebook COO Sheryl Sandberg cited this case too in her recent TEDWomen Talk, “Why We Have Too Few Women Leaders,” which I wrote about and has been the buzz among women across Silicon Valley.)

The media doesn’t help women feel okay about power — a point that Jennifer Siebel Newsom nails in a new documentary called Miss Representation. The film, which I saw on Saturday at the Sundance Film Festival, presents women leaders in politics, news, entertainment, and business — among them, Condoleezza Rice, Katie Couric, and Google VP Marissa Mayer — as well as top scholars talking about how the media objectifies women. The main message is that the media leads girls to care more about beauty and sexuality than their capacity to become leaders.

Miss Representation is a searing critique, but it’s upbeat at the end. Along comes Jessica Shambora, a Fortune writer featured as a confident young woman who is eager to inspire the next generation.

Jess, I assure you, is comfortable with power: She has worked, enthusiastically, on Fortune‘s Most Powerful Women list since she arrived at the magazine in 2008. (She started as my protegé and has moved way beyond that role.) On the way out of the theater, I thanked Newsom, Miss Representation‘s producer-director-writer, for spotlighting Jess. “I saved her for the end,” Newsom said, adding, “Yes, she’s a symbol of hope.”