A pluggable database is transported between a source DBMS and a destination DBMS, in a way that minimizes downtime of the pluggable database. While a copy of the pluggable database is being made at the destination DBMS, transactions continue to execute against the pluggable database at the source DBMS and change the pluggable database. Eventually, the transactions terminate or cease executing. Redo records generated for the transactions are applied to the copy of the pluggable database at the source DBMS. Undo records generated for at least some of the transactions may be stored in a separate undo log and transported to the destination DBMS. The transported pluggable database is synchronized at a destination DBMS in a “pluggable-ready state”, where it may be plugged into the destination container DBMS.