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You can also click on All Search Options in the Book travel on alaskaair.com. That will give you the additional option of searching for specific minimum fare levels under the Upgrade Type dropdown. MVP Gold guest (GGU eligible) will return K or higher fare classes in addition to the lowest main cabin fare, for example.

Note that MVP instant upgrade fare classes are the same ones that give a 50% Class of Service bonus and MVP Gold instant upgrade fare classes give at least 25% CoS bonus, so in addition to using them for instant upgrades, you can also use that option to filter for those class of service bonuses. Also note that there is website logic that limits the number of passengers in the search box (2 for MVP Gold instant upgrades, 1 for MVP instant upgrades) to the number that can be upgraded even if you just want the CoS bonus.

Another option is to purchase the ticket and then call in within 24 hours (if not Gold/75K or you have other pax on the ticket who are not Gold/75K) to upfare to the desired fare class. The call center ticketing fee would not apply because it's already purchased and the change fee also wouldn't as it's within 24 hours of purchase.