The good news for gay men? A new analysis of U.K. data shows they are more likely to be supervisors and managers than their straight counterparts.

The bad news? Gay men are far more likely (7.9 percentage points, to be exact) to be stuck in low-level management jobs at the bottom of the organization chart or at smaller, less prestigious organizations — the shift manager at a retail store, for example. They’re significantly less likely (2.2 percentage points) than straight men to be high-level managers — the people who run trading floors and manage entire regions.

The worst news? Gay men of color are hit hardest. They face an even worse disparity than you’d expect based on adding the gap for gay men to that for men from racial minorities.

To map these glass ceilings, researchers in Britain analyzed the responses of more than 645,000 working age adults to the annual U.K. Integrated Household Survey from 2009 to 2014.

Thanks to the survey’s size, it included more than 6,000 respondents who identify as gay, lesbian or bisexual. Combined with the U.K. survey’s detailed questions about management responsibility and sexual orientation, the large sample allowed for analysis which would not be possible in the U.S...