That is: directors who (while they may be named in passing) do not have their films mentioned or taken into account in David Bordwell, Janet Staiger and Kristen Thompson's long-canonical survey The Classical Hollywood Cinema: Film Style and Mode of Production to 1960 (London: Routledge, 1985). I've gathered the information through re-reading the book, as well as by performing word searches for all the titles in the directors' bodies of work, via Google Books.
To be periodically updated...
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Dorothy Arzner
.
E.g.: Dance, Girl, Dance (1940)
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Leo McCarey
E.g.: The Awful Truth (1937)
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Oscar Micheaux
.
E.g.: Body and Soul (1925)
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Max Ophüls
.
E.g.: Letter From an Unknown Woman (1948)
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Nicholas Ray
.
E.g.: Johnny Guitar (1954)
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Robert Rossen
.
E.g.: All the King's Men (1949)
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Frank Tashlin
.
E.g.: Will Success Spoil Rock Hunter (1957)
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Jacques Tourneur
.
E.g.: Out of the Past (1947)
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Robert Wise
.
E.g.: The Day the Earth Stood Still (1951)
.
