Finely woven

"The hat known today as the Panama hat was produced in Ecuador as early as the seventeenth century. Straw hats woven in Ecuador, like many other 19th and early 20th century South American goods, were shipped first to the Isthmus of Panama before sailing for their destinations in Asia, the rest of the Americas and Europe, subsequently acquiring a name that reflected their point of international sale, 'Panama hats', rather than their place of domestic origin"

en.wikipedia.org/wiki/Panama_hat

After bleaching, the hats are left to dry inside out. They are then heated on a press to obtain their final shape.

Homero Ortega Panama Hats, Cuenca, Ecuador

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