Two Israeli scholars have put their necks on the line to try to answer one of the most controversial questions in Orthodox Judaism today: what role can women take in public worship?

In the last decade, around two dozen "partnership minyanim" have been founded in Israel and the USA. These congregations have tried to pioneer services that increase women's participation, while operating within the parameters of Orthodox religious law. But they have faced two major problems.

The first is the difficulty in working out what constitutes an acceptable innovation when halachah is generally learned from texts written hundreds of years ago, long before modern notions of gender equality. The second is the response of critics to this difficulty: they say that congregations are simply making up the rules as they go along.

Keen to address both issues, husband-and-wife team Michal and Elitzur Bar-Asher have spent months poring over halachic texts, from the era of the Mishnah to the present day, gathering references to women's involvement in public worship.

"Many of these issues can be very confusing," says Ofira Krakauer, an organiser of Darchei Noam, a congregation in the Israeli town of Modi'in, where women lead large parts of the service. "People need help to know what can be done that is based in text. Until recently, it has been very difficult to find anything accessible written on this. The fact we are starting to see material emerging is part of a natural and positive process."

Despite the apparently daunting task in hand, "we were always surprised to see how many references there were", says Mr Bar-Asher. "This is because rabbis have always liked to approach every topic methodologically, and answer in many responses whether a woman can do such-and-such. They probably never dreamed that she actually would, but that's not what matters in halachah - the important thing is whether it's allowed or not."

Mr and Mrs Bar-Asher are graduates of religious higher education in Israel - he from yeshivot Har Etzion and Mir, and she from seminaries Midreshet Lindenbaum and Matan. They are now studying for doctorates at Harvard and Yale respectively, and attend a local partnership minyan.

Using the references they found as a basis, they authored the Guide for the Halachic Minyan, which is published in Hebrew and English on kipa.co.il, the Israeli website for the modern Orthodox community.

The guide works comprehensively through the year, starting with weekdays, then moving to Rosh Chodesh, Shabbat and through the various festivals. It gives a green light for women to lead part of the morning service, read from the Torah, and chant the haftarah. Women may say kiddush and havdalah, recite Hallel on Rosh Chodesh, lead Yizkor and call notes for shofar-blowing on Rosh Hashanah.

Pre-empting critics, Mr Bar-Asher admits they are "coming to halachah with an agenda", which he explains as wanting to redress the disparity between their beliefs "in every other area of our lives, namely gender equality, and in our religion". But he insists this is legitimate. "The important thing is that we are obligated by halachah and recognise that we can't actively change any existing rules. That does not mean there is anything wrong with searching to find out if there are things that sources allow women to do which they just don't tend to do."

According to the rules of halachah, the main obstacle to women leading prayers is that the leader must fulfil various obligations of prayer on behalf of the other worshippers. Only a person personally obliged to carry out a certain mitzvah may, by extension, do so for somebody else as well. As women are free from many obligations of prayer, they cannot fulfil these precepts for men.

Part of the guide consists of parts of the service where this principle appears prohibitive, "but for which women's leadership is in fact explicitly licensed among some - if in certain cases only a minority - of halachic decisors", says Mrs Bar-Asher.

This grouping includes Kiddush Levanah, the blessing over the moon, which is widely regarded a men-only affair because the popular halachic text Mishnah Berurah explicitly states that women may not take part. The Bar-Ashers bring an alternative authority, the Hochmat Shlomo, who says that women can lead the prayer for both men and women.

The same ruling applies for a second category, which consists of unisex obligations that rest on both men and women, such as saying kiddush.

The fact that synagogue tradition has evolved over time to include many parts that are customary, but not halachically required, accounts for a third category where women can lead for both men and women. Theoretically, such parts may be left out if time is tight, and given there is no halachic obligation being fulfilled here - never mind a gender-specific one - the Bar-Ashers see no reason why they cannot be led by women.

This principle is cited to justify female leadership of the Kol Nidre in Ashkenazi communities, and of the Kabbalat Shabbat service which, since the 16th century, has come to precede the evening service on Friday.

Most interestingly, the Bar-Ashers cite this principle to permit women to lead many of the liturgical poems included in the High Holy-Day prayers. "A good practice here is for services to have two chazanim, one male and one female, on the respective sides of the mechitzah," says Mrs Bar-Asher. "The man can lead the ‘halachic core' of the service and the woman can lead the rest."

Mainstream Orthodoxy has kept additions like these within the men-only domain. The arguments are variously that widely-observed traditions acquire status of halachah; that it is immodest for women to lead prayers; and that it is prohibited to revise established norms in synagogue.

However, partnership minyanim have rejected these viewpoints. The notion that it is immodest for women to lead prayers is based on certain strict halachic opinions, and is countered by lenient opinions, claims Mrs Bar Asher.

As for the accusation that they disregard tradition, her husband charges: "People are strangely selective about where to stick with tradition. Everybody rushes to raise this point regarding women's involvement, but much of the modern Orthodox world has chosen to completely change our pronunciation in prayer from that of our parents and grandparents to modern Hebrew accents for the sake of Zionist ideology. Why should this be legitimate but not trying to involve more than 50 per cent of the Jewish community?"

Since the guide was published earlier this year, the couple have received a constant flow of correspondence. "I just got an email from a woman who wants to make kiddush in her house, whose husband says that she's deluded if she thinks a woman can do that," says Mrs Bar-Asher. "She wants the sources to present. If that's a process we're helping, then producing the guide has been a useful exercise."