The Global Institute for Women’s Leadership advised LinkedIn on research out today which looks at gender differences in the way that men and women react to language in the workplace, as well as the different benefits people look for when deciding to apply for a job. The results suggest that men and women are much more similar than you might think.

Myth 1: Women aren’t motivated by salary

Received wisdom holds that women “just don’t prioritise salaries”, but this research found that when considering job postings, women were actually slightly more likely than men to value salary (80% vs 75% respectively).

So how then to explain research which suggests that when it comes to pay, women are on the back foot from day one? The traditional answer is that women just don’t ask for higher wages. One study of graduating professional school students found that while 57% of men attempt to negotiate their starting salary, just 7% of women did, with huge implications for eventual pay levels.

The latest evidence suggests a rather more nuanced view – and one that moves us on from the idea that “women don’t ask”. A large study with a representative sample of over 4,000 employees across 800 Australian workplaces found that women asked for raises just as often as men, but were less likely to be successful. Women who asked were given raises 15% of the time, compared to a 20% success rate for their male colleagues.

Asking can also be riskier for women than it is for men. Researchers at Harvard and Carnegie Mellon University carried out a set of experiments where they asked participants to rate men and women with identical CVs, and videos of male and female candidates negotiating their pay. The participants were more likely to view the female candidates negatively, and men were more likely to want to work with the women who accepted their initial offer of compensation, over those who attempted to negotiate.

So, what does this mean for companies who are looking to embed gender equality into their recruitment and reward processes?

First, we need to abandon the idea that any gender difference in negotiation is down to a lack of confidence. For a long time the prevailing advice has held that women need to “lean in” and behave more like men in order to receive the same rewards. This advice not only misdiagnoses the problem, but also prescribes a solution which, on its own, might do more harm than good.

Next companies need to ask how they can de-bias their compensation systems. As a rule of thumb the more opaque the process, the more gender-unequal the outcomes. One clear and concrete step companies can take is to state explicitly whether wages are negotiable. In one experimental study with 2,500 job seekers, researchers published a job advert across a variety of online job boards. In half the cases the job advert explicitly stated that the pay was negotiable. In the other half it did not. Among the job seekers who saw the advert without any statement of negotiability, men were far more likely to negotiate than women. Among those who saw the advert with an explicit statement of negotiability, women were just as likely to negotiate their salary as men.

Myth 2: Work-life balance is just for women

Flexibility is mostly associated with women, but as this research from LinkedIn demonstrates, it is increasingly important to the recruitment and retention of men too. This study found that 50% of men consider the availability of flexible working when looking for a new job, not far off the 60% of women who answered the same.

Offering flexible work makes good business sense. Fathers who work flexibly are more satisfied with their work-life balance than those who don’t, and this in turn is associated with lower intentions to leave the organisation. Some evidence suggests that there is a “hidden father churn” – fathers or expectant fathers changing employment because they cannot reconcile family and work obligations. And this effect is only likely to get stronger as millennial fathers are more likely to consider childcare responsibilities before accepting a new job, and younger fathers increasingly expect their employers to provide flexibility. Nor is flexibility just for parents, as more and more employees of all ages, career and life stages are seeking out ways of working that create good work-life balance.

So employers who want to stay ahead of the game, attract top talent and cultivate a happy, productive and stable workforce need to be explicit about publicly recognising and supporting male and female employees’ caring responsibilities and work-life balance.

Diversity efforts have often focused on treating men and women differently, assuming they have different priorities. But what this research suggests is that both men and women equally want well-paid jobs that fit in with family life. The key to achieving equality in the workplace, then, is recognising this and shifting towards a culture which emphasises flexibility for men, and which doesn’t assume that it’s natural for women to settle for less when it comes to salary.