If you want to ensure that your preferred website appears on the listing, you should make sure it is the only official website for your business across the Web.
If I am reading this correctly, this means that you should not have 2 different websites in your Google + profile. Is this correct? If so how would you get 2 websites with Markup? Have 2 different Google + accounts? What about if you own 2 different URL's and have contributor to for both of them. Would that be a red flag also?