Senior Anglican bishops have significantly watered down proposed concessions to those in the Church of England who are against women bishops.
It is hoped the proposals - to consider the views of individuals and lobby groups - will allow for agreement ahead of a planned vote in November.
Meanwhile, a BBC poll suggests nearly 80% of people support women bishops.
But one in five would have a less favourable view of the Church if women were not allowed to become bishops.
Legislation thrown out by the Church of England's General Synod in July would have given traditionalist parishes significant exemptions from serving under a woman bishop.
It came after pro-women campaigners objected to an amendment to the draft law - altered by the Synod's House of Bishops in May - allowing parishes who do not accept women bishops to request a male bishop who shares their beliefs about the ordination of women.
The latest proposal gives future women bishops more control in selecting a substitute for a particular parish, and would oblige them only to respect theological objections.
BBC religious affairs correspondent Robert Pigott says the bishops are making a finely judged calculation and, taking a gamble, the traditionalists will not be able to muster the one-third of Synod members needed to block the measure at the final vote in November.