Most people don't like to fly in the very early morning or on "red eye" overnight flights
If you don't have to arrive or return on specific days, then you can usually get a better rate flying on a day that is less crowded (usually Tuesdays, Wednesdays and Saturdays).
The earlier that you know you will need a ticket, the better chance you'll have of getting the best price.
Smaller airports on the outskirts of cities often are less expensive to fly into and out of than the main airport.
If you're not on a tight schedule, sometimes flights with stopovers will be less expensive than direct flights.
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visit that airline's Web site directly.
they can find something that you missed in your own searches.