How do I avoid the white line that forms around objects I've separated from a background?

Question

This is a cropped corner of an illustration I removed from its opaque background and placed on a transparent background.  The north and west borders show the whilte line that forms whenever I place objects on a transparent background.  The south and east borders are the cropped edges -- they are clean and make the trasition from object to background color without that white line.  With some objects, it's possible to use the Plygonal Lasso Tool, for instance, and trim that object away from the background.  With portraits or irregularly shaped objects, though, it's necessary to use the Magic Wand or other means to trim the background away from the object, which results in that unwanted white line.  I've read for hours online about this problem and have found no true resolution: Defringing, Removing White Matte, Anti-aliasing, trying to predict what color you'll lay the silhouette on and working in that color, and on and on.  It seems as though Photoshop would be relied upon heavily by professionals who need to place objects on top of one another without intrusion.  Does anyone have a method that really works?

Answer 1

Hi!  If the solutions you mentioned aren't working for your project, it might be worth learning a little bit about Layer Masks.  This is a page that explains how Layer Masks work. http://helpx.adobe.com/photoshop/using/masking-layers.html 
A Layer Mask is a black-and-white image that corresponds to your source image applied in such a way that white areas display and black areas don't.  So for your project, you would want to use Photoshop to turn your scanned illustration into a black-and-white image where the area you want to keep is white, and the area you don't want to keep is black.  Here is a demo using your uploaded image:
1. Open your image in Photoshop.  Right-click on your source layer in the Layers Palette and select Duplicate Layer. 
2. With the upper layer selected, use Image -> Adjustments -> Desaturate to turn the layer black-and-white. 
3. Use Image -> Adjustments -> Invert to reverse the black and white.  Now the white background should be black. 
4. With the upper layer selected, use Image -> Adjustments -> Levels.  Move the black, white, and gray arrows such that there is a hard black-and-white contrastwhere you want the white background to be removed. 
5. You may have to use the lasso tool or the brush tool to complete the silhouette of the image against the white background. 
6. With the upper, black-and-white layer selected, Edit -> Select All and Copy.  Turn the layer visibility off so that you are again looking at the original image. 
7. With the lower layer selected, click the Layer Mask icon.  Alt-click on the Layer Mask to edit the Mask directly. 
8. Edit -> Paste to apply the black-and-white image you created as a Layer Mask.  If you then click the layer icon again, you should be looking at your correctly cropped image!
Hope this helps.