Plastic Wall Anchors Without a Collar
I really hate the anchors that come with most wall accessories.  I always throw them away and opt for my own anchors.  I love the self tapping screw in type. They look like an over sized masonry or self tapping screw. So easy to use, simply insert the sharp point on your mark, no drilling required and use a #2 phillips screwdriver to screw them into your drywall. They come in different weight ratings. I use the 40 pound rated ones for most everything. They tighten snug to the wall and accept a #6 or 8 screw of your choice.(the kit comes with three different color screws) I buy them at Lowes, but unfortunately I don't have any original packaging with the brand name on them, but I will find out and post it in a comment later. They also work great when you have an existing hole from a previous anchor failure, as long as the hole is not much more than 3/8 inch in diameter.