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• a  without a brim
  a brimless hat

• Architects have designed prefabricated all-steel trailer houses, houses that would come in packages, factory-built "bubble" houses looking like brimless derbies.
• In their ankle-length gowns and brimless felt hats, they nimbly crossed rock-strewn slopes, driving herds before them.
• He was the jolly old fellow with the brimless plug hat.