Easing into the New Year, one big hope we have for 2013 is that women continue to bridge the gender gap in terms of pay equality and access to leadership positions. So much of the news was good last year: women were better educated than ever, we continued to claim coveted CEO roles at companies such as IBM and Yahoo, and one study even reported that women were the primary breadwinners in a majority of households in the US. That sounds like progress.

Yet, in order to clear a path for greater advancement and parity in 2013, we need to address the difficult paradoxes that women leaders continue to face — these are the mixed messages and uncomfortable realities that complicate an arguably positive picture of progress.

1. The Pay Paradox. According to the latest figures, women are better educated than ever, earning almost 60 percent of all college degrees. Yet, we are paid 23% less than men on average. Some of the gap can be attributed to career choice: more women than men choose to go into teaching and social work, for example, which pay less relative to “male” professions such as finance and technology. But career choice does not fully explain The Pay Paradox. An analysis of full-time workers 10 years out of college, for instance, found a 12 percent difference in earnings that was entirely unexplained by choice of profession. The bottom line is that progress in wage equity has hit a wall.

2. The Double-Bind Paradox. Women must project gravitas in order to advance at work, yet they also need to retain their “feminine mystique” in order to be liked. Perhaps surprisingly, of all the stereotypes that women encounter, this is the one that most women tell us about in coaching situations. Research by Catalyst confirms that gender stereotypes make it difficult for female leaders to feel comfortable taking a commanding stance because they are perceived as either competent or liked — but rarely both. As Forbes recently noted, “Studies show that assertive women are more likely to be perceived as aggressive; that women usually don't ask for what they deserve but when they do, they risk being branded as domineering or, worse even, “ambitious.” These are the double-bind dilemmas that we as a society need to banish before women can contribute fully within organizations.

Learn the remaining four paradoxes from the Harvard Business Review article.