WALL STREET’S glass ceiling cracked at last on March 1st, as Jane Fraser took charge of Citigroup, becoming the first woman to head a big American bank. That cracking sound has also been echoing across the rest of America Inc. Last year Carol Tomé became boss of UPS, a package-delivery giant. In January Rosalind Brewer became only the third black woman ever to run a Fortune 500 company (Walgreens Boots Alliance, a pharmacy chain). A month later Thasunda Brown Duckett was picked to run TIAA, a big pension fund.

Yet despite progress for women in the workplace, America still has a long way to go according to The Economist’s latest glass-ceiling index, which ranks conditions for working women across 29 countries. As usual, Nordic countries performed best overall in our ranking, with Sweden, Iceland, Finland and Norway taking the top four spots. At the bottom is South Korea, which scored just 25 out of 100 on our index, less than half the average for the OECD club of industrialised countries.

America received poor marks on parental leave and political representation. But it has a high share of women in management (41%) and on company boards (28%). In both cases America outpaces egalitarian Germany, which in January enacted a quota for female board members (and where the shares for management and board­rooms are 29% and 25%, respectively).

On average, just one in three managerial positions across the OECD’s 37 members is occupied by a woman. A recent study by SIA Partners, a consultancy, found that in Britain bias against women in senior corporate hiring remains systemic, with job ads for high-ranking positions using more “masculine” words that make them less appealing to women.

At least signs of progress can be seen even in traditional laggards like Japan. Mori Yoshiro had to resign as chief of the Tokyo Olympics in February after he complained that women talked too much in meetings. A woman replaced him.