The cheapest days to book Southwest flights are typically Tuesdays and Wednesdays. Airlines often release new fares and sales on Monday evenings, and by Tuesday, competitors adjust their prices, making it a good time to find deals, according to Commudle. Flights departing on Tuesdays, Wednesdays, and Saturdays are also generally more affordable due to lower demand on these days. 

Here's a more detailed breakdown:

• Tuesdays and Wednesdays:
  Airlines, including Southwest, tend to release new fares and sales on Monday evenings, with Tuesday being a prime day to find discounted tickets. 

• Saturdays:
  Flights on Saturdays are also generally cheaper than those on Fridays or Sundays because they are considered lower-demand travel days. 

• Advance Booking:
  Booking 3-6 weeks in advance can also lead to lower fares, especially when combined with flying on midweek days like Tuesdays or Wednesdays. 

• Flexibility:
  Being flexible with your travel dates can also help you find better deals. Consider checking various departure days and times, including early morning or late-night flights. 

• Southwest's "Discount Den" and Promotions:
  Subscribing to Southwest's "Discount Den" or keeping an eye out for their sales and promotions can also help you find even better deals, says AirTrackBot. 

Phone Booking:
Sometimes, exclusive fares or flash deals are easier to access by phone. You can try calling Southwest directly to inquire about these deals, suggests Commudle.