LGT CREW REFUSED A RERTE BECAUSE OF FUEL REMAINING AND DECLARED MINIMUM FUEL.

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N OF STL; ATC ADVISED RERTE. ON COURSE; FUEL WOULD HAVE ARRIVED DFW AT 10.2. THE RERTE WAS DECLINED. ATC SAD THAT MIGHT NOT BE GOOD ENOUGH; THAT EMER FUEL DECLARATION MIGHT BE REQUIRED. I SAID THAT COULD BE DONE IF MINIMUM FUEL WAS NOT GOOD ENOUGH. ATC RESPONDED WITH A CLRNC TO DFW VIA DIRECT FSM BUJ ARR; WITH MINIMUM FUEL. I ACCEPTED AND VERIFIED MINIMUM FUEL. ON HDOF; THE NEXT CTLR CLRED ME TO DFW DIRECT AS AN EMER. I RESPONDED THAT FLT WITH MINIMUM FUEL WAS NOT EMER FUEL. EACH SUBSEQUENT CTLR HANDLED ME AS AN EMER IN SPITE OF THE MINIMUM FUEL UPDATE. THE LNDG WAS UNEVENTFUL; AND TWR AND GND AT DFW EACH HAD TO BE ASKED TO SECURE THE UNNEEDED CRASH FIRE RESCUE EQUIP. EVEN WITH THE DIRECT DFW OVER STL; OUR ARR FUEL WAS 10.9. NOT ENOUGH TO HAVE TAKEN THE RERTE AND CHANCED OUR DEST AND ALTERNATE WX TO DETERIORATE. THERE WAS METERING IN EFFECT FOR THE NORMAL ARRS. I SUGGEST THAT WHEN A MINIMUM FUEL SIT OCCURS; THAT THE PROPER TERMINOLOGY BE USED AND THE PROPER PROCS FOLLOWED. THE ATC CONTINUING THE EMER FUEL STATUS OF THE FLT WAS NOT REQUIRED; AND CERTAINLY WASTEFUL OF THEIR RESOURCES AND OTHERS DISPLACED DURING THE OCCURRENCE (THEIR HANDLING HAD THE EMER BEEN THE ACTUAL SIT; WAS FLAWLESS!).