If you have a Southwest Airlines Rapid Rewards Account, you likely have a Chase Southwest Visa card. If not, get one. If so, here is what you can do--and lest you think there is anything sneaky about this, it was a Chase Southwest Visa rep, actually two of them, who explained this to me:
There are four cards: Consumer Plus, Consumer Premier, Business Plus, and Business Premier. When you open a new card, and spend a stipulated amount in the first three months (usually $1,000 to $3,000), you will get 25,000 to 50,000 bonus miles. You can then cancel that card within the 3-month period and pay no annual fee on the card. And these bonus miles count toward the companion-pass benefit. So, the only "cost" to you for doing this is the credit inquiry and you can do it for any card you have not applied for, so you can do it viz all three cards you do not have. When your card comes, if the noted bonus is only 25,000 miles, then be sure to call the number on the back of the card to see if Chase will up it to 50,000 or some other higher amount.
Note on the companion-pass perk: This is good for the year you qualify and the next full calendar year. So, you might look to racking up the bonuses in January to try to get to the perk as soon as possible in that year and be used in the following year as well.