...after filleting I would rinse and then let them soak in salt water for 10-15 minutes. Not sure why but for one it kept them from getting stiff. ...
If time permits, we have always soaked our fish in a salt water brine over night. It helps remove any remaining blood, slime, etc. in the fillets. Typically, we change the brine at least once. The first soak usually turns a little pink in a few hours. The fillets do get stiff by morning.