Vacancy or focus on M2M tenant?

[Christopher Giannino]

I'm looking into purchasing a duplex strictly for investment purposes (not going to be a owner occupant.)  Currently, one side of the duplex is vacant and the other side has a tenant on a month to month lease.  If all goes well and I acquire the property, should I look to fill the vacant unit first?  Or should I worry about properly screening the month to month renter?  I'm posing this question assuming that the month to month tenant pays their full rent on time and is not a "problem tenant."  I would think that I should focus first on filling the vacant unit and then put my efforts towards screening the month to month tenant but I'm looking to hear what YOU would do?