DALLAS—Brady Knowlton believes it's his inalienable right as a Texan to shove his bare hand into the mouth of a 60-pound catfish and yank it out of a river.

But wrestling a flapping, whiskered giant as it latches onto your arm with its jaws isn't among Texas's accepted methods of capturing fish. It is, rather, a class C misdemeanor, with fines of up to $500.

So...