Allen began her career as a messenger at Columbia Pictures in the early 1940s. Editing, like writing, was one place in pre-World War II films with a history of high-placed women (e.g., directors June Mathis and Dorothy Arzner began as editors; while Verna Field at Universal and Margaret Booth at MGM were editing pioneers). Allen was able to break in as a sound lab worker and assistant editor. With her husband, news executive Stephen Fleischman, she moved to France in the late 40s, where they remained for two years. Upon returning to the USA, Allen slowly began to win editing assignments, beginning with the short "Endowing Your Future" (1957) and including numerous industrials and the low-budget "Terror From the Year 5000" (1958). In 1959, director Robert Wise--himself a former editor--tapped Allen to cut his "Odds Against Tomorrow" which helped establish her in the business. Allen won particular praise for Robert Rossen's "The Hustler" (1961), in part for its creative and effective use of time dissolves. In 1967, Allen had what might be considered her "big break" working with Arthur Penn on "Bonnie and Clyde", a film in which the editing helped to create not just the necessary irony of the film, but also its numerous rhythms. While some moments are quite pastoral, the sequence wherein the Barrow Gang tries to fight its way out of an ambush was told entirely in rapid images and is considered a marvel of editing. Paul Newman then selected Allen as editor for his directorial debut, "Rachel, Rachel" (1968), which mixed the harsh world of Joanne Woodward's life with her daydreams. In 1969, Allen reteamed with Penn for "Alice's Restaurant" and went on to provide excellent work on his "Little Big Man" (1970), "Night Moves" (1975) and "The Missouri Breaks" (1976).

Allen first worked with Sidney Lumet on "Serpico" (1973), but is better remembered for her work on "Dog Day Afternoon". Again, Allen proved amazingly creative, changing the tempos of scenes and developing aural and visual relationships. Allen and Lumet were less successful creatively with the musical misfire "The Wiz" (1978). For George Roy Hill, she cut "Slaughterhouse Five" (1972) and "Slap Shot" (1977). The hockey sequences in the latter were particular marvels of cutting. Allen not only co-edited "Reds" but also served as one of its executive producers, working alongside Beatty on many creative choices for the film. She worked again with Newman on "Harry and Tonto" (1984) and for Robert Redford on "The Milagro Beanfield War" (1988). Allen shifted to independent films for "Henry and June" (1990) and later to special effects and highly-charged action for Barry Sonnenfeld's "The Addams Family" (1991). After a nine-year hiatus during which she worked at Warner Bros. as an executive, Allen returned to the cutting room to edit "Wonder Boys" (2000), for which she received an Oscar nomination.

Her two children are also active in filmmaking; son Tom Fleischman is a sound re-recording mixer and daughter Ramey Ellis Ward is a production associate.