Using Import (or importing a new alpha channel) is similar to and sometimes worse than the result you get with DXT1, so definitely try with the DXT3 or 5 import.

A fresh Bodyshop import can work fine, but it too can cause some artefacts on the texture, especially if reimporting textures from other CAS items. It depends on the quality of that texture, but also what you do with it. Bodyshop is also known for causing texture artefacts, especially around large areas of color.

If/whenever you make textures yourself, keep the workfiles (PSD/GIMP workfile, or similar layered format) and use those when making new versions or recolors, since that's the best base texture you'll get for that project.

Andrew, if you open the file in SimPE and find the texture file you want to replace (so you see the texture in the plugin view) - right-click on the preview picture of the texture itself. If you have the DDS utilities installed, this brings up a menu from which you select "Build DXT". That then shows a window where you can choose from a drop-down menu which includes DXT1/3/5 and a load of other options.

I don't think it's important really to understand what DXT is or what it means - unless interested - the above is what I have done previously to change textures within SimPE rather than BodyShop. For example, to update a skin tone to make it anatomically correct, without losing other aspects such as the genetic values.

If when you right-click on the texture image, you don't see the "Build DXT" option, I think that means you need to download and install the DDS Utilities.