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Dies: The dies are inserted into the press and are what allows the reloader to resize the brass, remove the spent primer, flare the case mouth (on straight walled handgun ammo), seat the bullet, and in some cases, place a crimp around the bullet. There are many manufacturers who produce quality reloading dies including RCBS, Lee, Hornady, and Redding, among others. Just be sure to get the right dies for the caliber you're reloading!
Case Tumbler: A case tumbler, along with brass cleaning media (usually ground corncob or walnut shells), offers an easy, effective way to clean brass prior to putting it through the reloading process. This is generally done for two reasons. The most important is to remove dirt and grime which can damage or "gum up" your dies. The other is to enable you to produce shiny, visually pleasing ammunition. It is also easier to spot case defects on clean brass (we'll discuss this more in-depth later). Tumblers are available anywhere reloading equipment is sold, and they all do the job. Select yours based on the number of cases you'll want to clean in a batch. Avoid using brass polishes which contain ammonia, as this can weaken the brass.
Case Trimmer: Generally, this applies mainly to rifle brass. Most handgun reloaders don't trim brass, but there are some that do. We will go more in depth into the trimming process later.