Unfortunately you cannot remove mercury from a fish. You can, however, reduce other types of contaminants (such as PCBs and dioxins) that you consume in the fatty tissue of fish by removing the skin and trimming away fatty areas of the fish. To do this, cut away all the fat along the back of the fish, slice off the belly fat, and cut away a V shaped wedge to remove the dark fatty tissue along the entire length of the fillet.
You can also reduce your consumption of other pollutants in fish by using cooking methods that allow fat-laden juices to drip away since drippings or broth may contain higher levels of pollutants. In addition, the frying of fish seals in pollutants that might be contained in the fat.
As far keeping yourself within the healthy mercury limits, please refer to the New Hampshire Department of Health and Human Services web page for the Fish Consumption Advisory Booklet 
(Fact Sheet ARD-EHP-25) which details the fish consumption limits for freshwater fish and ocean fish and shellfish.
There are more specific stipulations depending on the body of water that is being fished. Before consuming any caught fish check with the guidelines of that specific water body.
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