Next to madai, I would have to say that hirame is my absolute favourite fish. I especially love it served with the zest of yuzu and a dash of ponzu. As far as the fish itself goes, hirame, or fluke, is a flat fish. So unlike round fish, you get four fillets per fish, usually with the top and bottom cuts having a different colour, for one reason or another. [Something I'll have to look into someday.]
Like I've ranted about in previous posts, there is a specific cut in this fish that many itamae typically ignore, and that would be the Engawa, or the meat near the fin. Believe this or not, but in Japan, the Engawa is considered a delicacy. Perhaps it's because of the textural difference from the fillets (it's crunchy, as opposed to being soft and fleshy), or the fact that you can only get four slices per fish, but the Engawa sells for a little more than a regular cut would in Japan. But, in America, of course, all the good things are neglected and the worthless, or near worthless, things are prized. The Engawa is usually just discarded. Or, if it is saved, it's more often than not discarded anyway due to the lack of interest by the clientelle.