The council of Nicaea in AD 325 had to deal with disciplinary matters related to three schisms or heresies in addition to Arianism. The persons involved were the clergy among the followers of Meletius, Novatian, and Paul of Samosata.
The interpretation given in the standard history of the councils by Hefele and Leclercq is that the fathers at Nicaea did not require a new ordination of Novatian and Meletian clergymen who returned to the catholic Church. Their previous ordinations were valid but irregular. When this irregularity was corrected, the persons involved could then function in the clergy of the great Church. Later theory about the indelibility of ordination appears to have influenced unduly this interpretation.