how to finance 2nd investment property

[S B]

I own one investment property (duplex, if that matters) - It was quite an ordeal to secure the financing for it: a million questions about what other debt I have, etc. I ended up getting it because I had virtually 0 debt.

Now I'm thinking I want to buy a second one. But what happens when the lender learns I have a 160k mortgage? That obviously is much much more debt than I had last time when I just squeaked by... how does this work? If I can prove that I have tenants, does the lender then ignore/discount the mortgage debt it when qualifying me?