She first came to public attention in the 1996 Lynne Stopkewich film Kissed, in which Parker starred as a sympathetically portrayed necrophiliac. She received a Genie Award for her performance in the movie.

Parker has received much critical praise for her bravery in tackling difficult roles; for instance the aforementioned necrophiliac, a sympathetic lap dancer and paid escort in The Center of the World, and a female rabbi, Ari Hoffman on Six Feet Under.

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