Objects slightly misaligned when copying?

I’m trying to copy a few of the same cube shaped object to create a stack of them, and despite only moving them in the Z axis, they end up slightly misaligned, like almost un-noticeably so. I can’t fix it myself because despite having grid snapping turned off, it still seems to snap a minimum amount, so I can only choose between 2 locations to have the objects misaligned, and not the in-between that I need. I don’t know what is causing this so hopefully someone can help.

Okay apparently the cube was deformed somehow in Blender and now that is fixed. But I still have issues lining things up sometimes because I can’t completely remove grid snapping. How can I do that?