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Step 1: 'The Innocents' (1961)
Reason for placement: One of Martin Scorsese's 11 scariest films of all time is pretty tame by today's standards, initially playing like an elegant Victorian costume drama before moving into gothic horror territory (it's based on Henry James' "The Turn of the Screw"). The ending is look-through-your-fingers unnerving, but on the whole it's a restrained, masterpiece; if your subject can't handle this, there's probably no hope for them.
Why it will win them over: Deborah Kerr is compelling as a sexually repressed governess who becomes convinced that the two precocious children in her care are possessed by evil spirits; Freddie Francis's gorgeous cinematography and some chilling sound design create a hypnotic mood.
Crossover hook: The screenplay was written by acclaimed "In Cold Blood" author Truman Capote.
Follow-up recommendations: "The Haunting," "Onibaba," "The Others"