How to fix smooth edges on sprites?

Hi, Im having problems getting my sprites with transparent backgrounds to have smooth edges. It seems as if the semi-transparent pixels near the borders have been converted to a full alpha color and makes the borders of the sprites look wierd.

Here is an example:

Original PNG file:

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Screen shot from inside unity:

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Is there a way to fix this? is there a problem with my PNG files? any help would be great!

PD:

Don´t know why but this PNG file looks fine in game:

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Please do a more thorough search next time.

Here is a thread that is pretty in depth on why your problem happens, and how to solve it.

http://forum.unity3d.com/threads/2181-Photoshop-how-to-perfect-fringeless-alpha-perfect-edgelines