> What I´m trying to do is to get a smoth border (of a
> selection) that I will cut out a one picture and paste it into
> another one.
> When I do this, the borders get dark (black) and are easily visible
> on the new picture.

That's a common problem, particularly if the new background is lighter than the old one. This is the way I solve, or minimize, the ringing effect.

Here's the original, a bright daffodil taken against the background of a piece of dark foam core board.
http://www.pbase.com/image/27005825.jpg

I selected the nearly uniform background using the magic wand tool at a tolerance of 33%, selected the inverse, touched up the errors using the polygonal lasso tool, and moved the flower to a new top layer. You can clearly see the black ringing around the petals.
http://www.pbase.com/image/27005826.jpg

Let's go back a step. After the selection and cleanup, go to Select - modify- contract, and input a value of 2 pixels. Then, move the flower to a new top layer, and the ringing is gone.
http://www.pbase.com/image/27005827.jpg

I did this in my old copy of PSE 1.0.
--
Warm regards, Uncle Frank,
FCAS Charter Member, Hummingbird Hunter
Contributing Editor, digicamhelp.com
www.pbase.com/unclefrank/coolpix