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We explore several problems associated with persistent data structures. We show how to eliminate amortization from one of the data structures of Driscoll et. al. . We show how to make some new data structures, including disjoint-set union-find, partially persistent in optimal time and space. We eliminate amortization from dynamic fractional cascading. We explore a family of pebble games associated with persistence. One relevant version of this pebble game shows that randomization may be a useful tool for elimination of amortization.dblp:conf/soda/DietzR91 fatcat:f5a4pr63tzgqrivh7fu7ql3fiu