How can I add a texture with an alpha channel without affecting the base materials opacity? I'm trying to make this handle look dirty by using a texture with an alpha channel. It's actually adding some transparency to the base material which I want to look solid. 

I have tried changing the order of where I plug nodes into the sockets which only makes it worse.

Render

Seeing back edges

Nodes

Texture
You are so close!

Delete the transparency node and make suitable adjustments.




Above the nodes overlay color.  
The nodes select color by alpha channel.  
There is no desired transparency in the final material.
There is no need for any transparent shader.
Selecting color and final material transparency are different.