Amazon offers Prime members the Nine Stars Infrared Touchless Stainless Steel Trash Can, model no. DZT-50-9, for $29.98 with free shipping. (Non-members can spend $35 to bag free shipping; otherwise, it adds $11.90.) That's the lowest total price we could find by $33. This 13.2-gallon can detects hand movements within 10" and opens automatically.

Prime orders placed by December 22 are guaranteed to arrive by Christmas.