Catholic women say there’s a clerical stained glass ceiling in the Vatican, and they want to shatter it, Reuters reported yesterday.

They want to vote in major policy meetings. They want Pope Francis to deliver on his promise to put more women in senior positions in the Holy See’s administration. And some of them say they want to be priests.

“Knock knock! Who’s there? More than half the Church!” several dozen Catholic women chanted outside the Vatican on Oct. 3, the first day of this year’s synod of bishops from around the world.

A petition demanding that women have the right to vote at synods has collected 9,000 signatures since it opened online at the start of this meeting. It is sponsored by 10 Catholic lay groups seeking change in the Church, including greater rights for women and gays and a bigger role for the laity.

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“If male religious superiors who are not ordained can vote, then women religious superiors who are also not ordained should vote. With no ontological/doctrinal barrier, the only barrier is the biological sex of the religious superior,” it reads.

The role of women in the Church has been a recurring theme at the month-long meeting, which brings together some 300 bishops, priests, nuns and lay participants. Only about 35 are women.

The subject has come up in speeches on the floor, in small group discussions and at news conferences by participants in the gathering, officially titled “Young People, Faith and Discernment of Vocation”.

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Only “synod fathers”, including bishops and specially appointed or elected male representatives, are allowed to vote on the final recommendations to be sent to the pope, who will take them into consideration when he writes his own document. Other participants are non-voting observers, auditors or experts.

The Holy See, as the offices of the central administration of the 1.3 billion-member Church are known, and the State of Vatican City have a combined work force of about 4,100 people. About 700 are women.

Of the approximately 60 departments in the Holy See, about 10 must be headed by priests because they deal with governance and jurisdiction over other ordained ministers or other sensitive doctrinal matters, the Church says.

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Francis has promised to put more women in senior roles in those other 50 departments. But more than five years after he was elected, there are only six women in such roles. Five are lay women and one is a nun. None of them heads a department.

Francis told Reuters in June he had to “fight” internal resistance to appoint 42-year-old Spanish journalist Paloma Garcia-Ovejero as deputy head of the Vatican’s press office. He declined to name those who had resisted, but said he had to use “persuasion,” an apparent reference to the powerful conservative wing of what has been an institution run exclusively by males for 2,000 years.

The membership of female religious orders is about three times larger than that of male orders. The cause has won some influential clerical male backers.

At a news conference on Oct. 15, superiors general of three major male religious orders, the Jesuits, the Dominicans and one branch of the Franciscans expressed support for changes in synod rules in order to allow women to vote in the future.