(****) Baseball caps, often worn backward, are today’s fave lid. They range from classic Yankee to gold-lame versions.

(**) Known as softies or vagabonds, these squashy retro models might look better with a few fishing flies in the brim.

(***) These floppy, mod London sombreros should be worn with a brooch for best effect-and improved visibility.

(***) Besides being stylish, oversize straw bonnets are a hit with beachgoers who know enough to stay of out the sun.

(**) “The Cat in the Hat” meets haute couture. But is it a fashion statement or an accordion?