I initially thought there was just a minor leak, however the damage was fairly extensive. There seemed to be several potential leak sources, one of which is the roof to wall connection, that is part of another (kitchen) roof. There is a second roof that drains toward this lower shed roof.

Sub-standard construction complicated the repair. Luckily,  I had some old 1 inch                   thick by 6 inch wide deck planks that I could use to reinforce the roof structure.

I’m trying do a relatively modest repair here,  but the irregularities  are a  nuisance.                     The shed is made from salvaged materials.  I decided to go with  a 5/8 cdx plywood deck as I tend to avoid 1/2 plywood unless it is used over  tightly spaced planking.

This roof only measures about 8 x12 ft.  Rather than using mineral paper underlayment, I decided to use Libertybase Sheet. It is a superior product, but costs at least 5 times more than mineral paper. This base sheet can be installed without nails and it has an adhesive backing. The trick is to prime the deck with a special primer. The primer bonds to the wood and creates a substrate that the base sheet will adhere to. The base sheet bonds to the deck.  It will not be removable.

The Liberty Cap sheet has an adhesive backing that bonds to the base sheet so, no nails are required for this roof.  No nails = no holes and no way for water to get between the base sheet and plywood.