When I enable depth testing in my program I get this weird overlap effect. I gather it's something to do with blending but I don't know much about texture blending.
http://i.imgur.com/vBAtP.png
In the picture examples of my problem are circled.

Any help is much appreciated!
Thanks,
Rowan.

PS: As you can tell from the picture my top down tree sprites are awful. Do you know where I can get some the look decent.