Sweatbands in leather hats are there to prevent perspiration and body oils from staining the outside of the hat. Whether the band is made of fabric or leather, it will probably need to be cleaned frequently.
For fabric sweatbands, fold them down and clean with a mild detergent/water mixture and a soft brush. Use the brush to scrub the band and then blot with a clean white cloth dipped in water. Leave the band folded down until it air dries.
For leather sweatbands, fold it down and use a commercial leather cleaner to remove stains and odor. Follow package directions and allow to air dry. When the band is dry, use a leather conditioner or lotion to keep it supple.
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