Idioms and Phrases with one eye on
one eye on
Paying some but not full attention to, as in He ran the rehearsal with one eye on the clock. Also see have one's eye on; out of the corner of one's eye; see with half an eye.
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The American Heritage® Idioms Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.