I remember how much fun I had when I began finishing leather straps using an edger, zipping-through a pile of long straps, rounding all four edges.  I still enjoy doing that.

However, a common error newbies make is taking off the edges of the top surface of the straps with too-high-a-number edger, producing a furry, dull-looking edge that you can see in this illustration.  Either you will fine-finish the straps during the construction or the wearer will burnish the surface edges of the strap in wearing them.  I encourage you to enhance the presentation of your work by doing it before assembly.

I like to make 6 to 10 at a time, and after cutting them out and making the “eye"-end with a punch and a slit, tie them all to my firmly affixed sole cutter after I briefly wet them in my laundry sink.  

Then I use a hoof-brush (a saddlery tool) to make a lather in the saddle soap tin and brush it through the gathered straps, saturating the two edges of each strap as well as the two surfaces.  Tanneries call this “stuffing” the leather.  After most of the foam has been absorbed, I use a piece of denim or coarse linen, and stroke each of the straps many times, squeezing the rag tightly as I pull the straps through my hand and the coarse cloth.

This is a pleasurable task, perhaps even more fun than edging, and if you have left MOST of the top two edges with most of the top of the hide intact, you will burnish and polish the tops as well as having stuffed the strap with saddle soap that fills in the porous bottom surface and two edges, as well as the top layer.

Read about the makeup of skin, from your own to the tanned cowhide you are using

I advise you to take very little off the top edges, and leave more of the dense top-hide to burnish and polish.  I use a #0 or #1 edger for the finished surface and a #2 or #3 for the bottom or flesh surface.  They will hold their polished, compressed firmness and create a finished look and function of closing the pores of the edges.  If you use a larger-number edger on the top edges, and tilt your edger too high (flat), you will take off too much of this tightest, closed-grain part of the cross section.  So tilt your edger closer to vertical, whichever size edger you choose.  

The broad arch straps of the LotR design are finished the same way.  A final thin coat of neatsfoot oil helps to lubricate the fibres of the oak-tanned cowhide, but use it sparingly.  You can also add a small amount to your saddle soap tin when you are making a lather with water.  This will help the oil saturate the leather more deeply.