Bank statements and Pay Slips

My recently married wife and I are proceeding with our EEA family permit application. We have evidence of our relationship being genuine (one should hope), but my issue lies with bank statements...

I'm a junior software developer (freshly out of uni), and so travels to see my wife were rather costly. I'm sad to say I'm currently on my overdraft... never had to go on unplanned one, but nevertheless minus is a minus, and it doesn't look good despite my financial position being stable.

My payslips, on the other hand, look quite decent. I have to provide evidence of working in the UK... would payslips without the bank statements be enough? Or perhaps would it be OK to send off the bank statements and explaining a reason for the overdraft? Anyone know how this would impact our application?

Thank you for all your help in advance

Without checking the exact requirements I doubt you actually need to prove you have sufficient funds, or having to provide bank statements in the first place