only after excommunication 

The article currently states that people are rebaptized only after entering the Church again after excommunication. This is not always true. In addition to rebaptism after removal of one's name from church records* , a bishop may approve a rebaptism for a token of repentance rather than merely membership in the Church. A reference: [W]e had a wonderful older brother in my branch with a gambling addiction.   When he was finally able to overcome it, and despite no official Church punishment, he petitioned for and was granted rebaptism, to witness again to his God, his Church, his family, and (maybe most importantly) himself that he was born again.   Technically, all this good brother needed was the Sacrament of the Lord's Last Supper, but can't you imagine how much more staying power the Sacrament of Baptism and Rebirth has had on his determination? ()

* This administrative action was instituted, IIRC, in the late 70s or mid 80's. It is distinct from excommunication. Prior to this being available, however, a person had to be "voluntarily excommunicated" in order to remove that person's name from Church records, but this is no longer the case.