Now, use a small brayer to gently press the right and top edges of your 5" x 10" clay cup blanks. Now, carefully turn your blanks over and press the reverse sides of the top and right edges. This will give the top of your mug a refined look - and a rim as nice as that of a thrown cup. If you press too hard, you will create a sharp or unattractive edge. Practice with the brayer on bits of scrap until you achieve a nice, rounded look. Many handbuilt cups have a crude or ragged rim that detracts from the visual appeal of the cup.
This tool is not actually a proper brayer for printmaking use, but is a wall-paper seam sealer from the hardware store. They cost about $3, and are available made from wood or plastic - each works equally well.