The House of Bishops decided on Monday that any male bishop drafted in to minister to a parish must share that parish's theology - that is, Anglo-Catholics must be looked after by an Anglo-Catholic bishop.
The second amendment stressed that drafting in a male bishop to a diocese led by a woman bishop does not undermine her ministry.
However, the group Women and the Church (Watch) said the amendments "can only undermine the ministry of women in future years".
A spokesman for the traditionalist Catholic Group in Synod charged the bishops with failing to "accommodate the traditional orthodox position".
And the conservative Evangelical group Reform said that the group was "disappointed" the bishops had not implemented compromise options they had put forward.