A new study is further proof that the double bind female leaders face is more pervasive than we thought.

For decades, research has shown that women are penalized if they act too confident or dominant. Because these leadership traits are traditionally seen as stereotypically male, women who display them get unfairly penalized for going against type. As Marianne Cooper, the lead researcher for Sheryl Sandberg's book Lean In, wrote recently for the HBR Blog Network, "if a woman acts assertively or competitively, if she pushes her team to perform, if she exhibits decisive and forceful leadership, she is deviating from the social script that dictates how she 'should' behave."

But this well-studied phenomenon appears to be easing somewhat, write three researchers from Australia in a new paper in the British Journal of Social Psychology. It shows that while such penalties still exist, women aren't bowing to the pressures. In fact, women are now even more likely to be described by others as being assertive or dominant. They've also been shown to receive similar evaluations as men receive, despite displaying such leadership behaviors. In other words, it's becoming more socially accepted for women to be tough and commanding leaders. That's progress, right?

Perhaps. But in the new paper (which is partially titled "If you're going to be a leader, at least act like it!"), the researchers hypothesize there could also be a "previously unidentified drawback" to this greater acceptance of assertiveness in female leaders: "Specifically," they write, " that women who fail to display [assertive behaviors] may now be punished, a consequence that will not apply to men acting in the same ways."

And indeed, it seems they were right: Their studies showed that when female leaders act hesitant or tentative, they're penalized, whereas male leaders got a free pass for doing the same. In other words, they're damned if they do, and doomed if they don't.

In the new paper, the researchers performed two studies that presented students with a speech—one on climate change and another on raising university tuition. In one case, the speech was strongly worded and emphatic; in the other, qualifiers, hedging language, and "ums" and "you knows" were added to the same speech for a decidedly more tentative tone. Students were told whether the politician "giving" the speech was male or female, and were then asked to rate it on how likeable, influential and assertive the speaker seemed. In both studies, the tentative female speakers were deemed less likeable and less influential than both the assertive women and the tentative men. In addition, men fared about the same regardless of how assertive their speech was—meaning that, unlike the women, they weren't penalized for acting tentatively.

While the results may be depressing for women who've long been judged for acting too forceful and can now be dinged if they're not confident enough, there was some good news in the study as well. In this research, at least, assertive female speakers were rated similar to—or even better than—the assertive men in the study. As the authors write, "these findings signal a turnaround from times when endorsement of traditional gender roles was greater." And that, at least, is progress.

Jena McGregor is a columnist for On Leadership.

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