It's well-established that women face more obstacles climbing the corporate ladder than men do. But a myth still persists that once they reach the top, they'll enjoy the same power as male leaders. That's rarely the case, though. And in fact, according to a new Boston Consulting Group (BCG) study, certain aspects of women's jobs go downhill as they get promoted. BCG surveyed 345,000 people on their levels of engagement at 36 companies, measured by factors including their relationships with their colleagues, their opportunities for advancement, and their coworkers' appreciation for them. Among the companies where employees felt most engaged, the results were similar for men and women. But those ranked in the lower three quartiles had senior-level women who were less engaged than their male counterparts, Fortune reports. This gap existed in 69% of companies. At these workplaces, the engagement of senior women managers was 4% higher than it was for non-managers, whereas men saw a 12% engagement boost as they gained seniority. Upper-level women particularly felt like their opinions weren't valued, their accomplishments weren't recognized, there wasn't a sense of camaraderie in their offices, they lacked mentorship opportunities, they had fewer shots at promotions, and their work-life balanced diminished. While men felt like their coworkers supported their pursuits outside work more as they became more senior, women felt they lost support. "When companies get engagement right, everyone benefits. When they don't, senior women feel the pain disproportionately," the authors conclude. This isn't the only way work can get tougher for women throughout their careers. An Earnest study found that there's a higher pay gap in management roles. It's yet another reminder that leaning in alone won't solve workplace sexism. Companies need to create a better environment for women to lean into.