The second section of the first chapter of Christus Dominus treats the relationship of the bishop with Rome. First, a nod to the authority of the local bishop: pretty much everything that Rome hasn’t already covered:
To bishops, as successors of the Apostles, in the dioceses entrusted to them, there belongs per se all the ordinary, proper, and immediate authority which is required for the exercise of their pastoral office. But this never in any way infringes upon the power which the Roman pontiff has, by virtue of his office, of reserving cases to himself or to some other authority.
The general law of the Church grants the faculty to each diocesan bishop to dispense, in a particular case, the faithful over whom they legally exercise authority as often as they judge that it contributes to their spiritual welfare, except in those cases which have been especially reserved by the supreme authority of the Church.
Curia, enter stage right in Christus Dominus 9
In exercising supreme, full, and immediate power in the universal Church, the Roman pontiff makes use of the departments of the Roman Curia which, therefore, perform their duties in his name and with his authority for the good of the churches and in the service of the sacred pastors.
However, the Vatican Council recommended these offices be reorganized and adapted for the needs of the present, presumably to keep the notion of service to the local bishops and their dioceses at the forefront. CD 10 suggests these offices be widened from their Italian make-up, inclusive of a catholic Church, looking to diocesan bishops for curial department membership, and even lay people.
Finally, the fathers of the council think it would be most advantageous if these same departments would listen more attentively to laymen who are outstanding for their virtue, knowledge, and experience. In such a way they will have an appropriate share in Church affairs.
It would be good to see even more lay people, but note that the definition of what sort of share would be “appropriate” is left to the judgment of the pope and curial heads.