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I'm having trouble removing a white background with complex images like these ones. When I use the Magic Wand tool on them I just end up cutting way too much stuff away or not enough and leaving white (background) residue left on the image.
Is there any trick (with layer blend modes?) to get all of the white background away from it and keeping a nice clean image as a result?
In my opinion, the Magic Wand tool is about the worst method for extracting a background in 95% of all use cases. Unfortunately, I realize it is the "go to" method for many users. However, it's not often the "best" method, in fact it's among the worst. The Magic Wand method can work for hard edged objects without any cast shadows. But beyond that it's pretty horrible.
Channels are often easier and faster than any other selection technique if the subject is already isolated on white. Channels allow you to retain shadows and subtle drop offs in many instances.
So, to use channels...
Find a channel with decent high contrast... in this case I've chosen the Blue channel..
Command/Ctrl-click the duplicate channel thumbnail in the Channels Panel to load it as a selection.
Go back and highlight your Layer in the Layers Panel.
Hold down the Option/Alt and click the New Mask button ( 
) at the bottom of the Layers Panel.
From here you may need to go in with a brush and manually refine the mask in a few places.
For images such as this one with pronounced cast shadows....
You may need to extract the shadows to a separate layer to better control their appearance.
So I duplicate the masked layer twice...
On the first duplicate I go in with a brush and manually mask the shadows...
On the second duplicate I go in with a brush and manually mask everything except the shadows...
This gives me a separate layer to control the cast shadows.
With both these duplicate layers visible, you can alter the blending mode and/or opacity of the shadows to better the overall appearance.
Both these image took roughly 30 seconds each to mask. The second image took maybe 1 or 2 minutes to refine the mask for shadows, but it could use a bit more time.
If you have Photoshop CC, then you could use the Select and Mask functionality to refine a selection made with the Magic Wand.
Select the Magic Wand, deselect the "Contiguous" option, set the Tolerance to 20, and click on a white area
Select > Invert
Click on Select and Mask, set the View to: On Black, at 100%
Select the Refine Edge Brush tool, make the brush large using the square bracket keys to adjust the size.
Click on the background area and without releasing the mouse button, paint over all the areas where the background meets the subject, to remove all the remaining white background. Release the mouse button when it looks good.
Set Output to: New Layer and Layer Mask
This will create an almost perfect mask, without any halos of white, and just the right amount of transparency around the edges so you can place it over any background image you desire.
Here's an example showing the use of the Refine Edge Brush, creation of the mask, and then toggling the mask on and off.
