It has been three months since the Church of England's independent reviewer criticised Wakefield Cathedral, which had stopped publishing the name of the celebrant in advance.
The report, by Sir William Fitall concluded that details of celebrants "should not be regarded as confidential information" and "should be supplied with good grace to anyone who asks for it in advance".
The report said the Cathedral's policy didn't properly reflect the Anglican Church's commitments to traditionalists when the ordination of woman was approved thirty years ago.
After consultation and reflection, the Dean has decided "to keep the existing policy in place" and so will not restart publication of the list of celebrants.
Rev Cowling maintains the change he is making as "a significant adjustment which I believe to be in line with the spirit of (Sir William's) conclusions"
In a three stage process, people will have to be regular worshippers at the cathedral, have a face-to-face meeting with the Dean and confirm they want to avoid communion services celebrated by a woman priest based of "reasons of conscience".
Only then will the Dean decide whether to start sending the individual a list of who will be taking which services. But, with the condition that the list isn't circulated more widely.
The Dean has revealed he has met with Dennis Belk, with the person who launched the complaint. Mr Belk is said to be "reflecting on this offer".
Anglican traditionalist group Forward in Faith has welcomed the Dean's statement as a "first step", but says it hope for "even greater generosity in future".
Dennis Belk told Premier his views are reflected in the statement from Forward in Faith but declined to give any further comment.
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