B737 FLT CREW DECLARES MINIMUM FUEL WHILE ON OFF-COURSE VECTORS.

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I DECLARED MINIMUM FUEL WITH ZNY. I DID SO BECAUSE I BELIEVED THE SLOW STEP CLBING AND AN EXTREME OFF-COURSE VECTOR; 180 DEGS TO OUR DEST; HAD PLACED US IN A SITUATION WHERE; UPON ARR AT OUR DEST; WE WOULD BE UNABLE TO ACCEPT ANY DELAYS DUE TO LOW FUEL IN ACCORDANCE WITH THE FOM. DESPITE THE FACT THAT WE TOOK A 1 HR DELAY OFF THE GATE AT LGA WE MANAGED TO TAKE OFF WITH OUR CLRED FUEL OF 19.8 LBS BECAUSE WE CONSERVED FUEL BY SHUTTING DOWN THE ENGS WHILE HOLDING. THIS FUEL LEVEL WAS THE ABSOLUTE MINIMUM THAT I WAS WILLING TO ACCEPT AND WAS LIMITED BY TKOF PERFORMANCE ON RWY 31 AT LGA. SINCE WE HAD ALREADY BEEN GIVEN FUEL FOR A LENGTHY RERTE I FELT WE COULD GO WITH THIS FUEL AND HOPE TO GET SOME SHORTCUTS ALONG THE WAY TO SAVE GAS. OTHERWISE WE WOULD HAVE HAD TO BUMP REVENUE TO ADD MORE FUEL. AFTER DECLARING MINIMUM FUEL; ATC ASKED IF WE WANTED TO RETURN TO LGA AND I EXPLAINED THAT WE COULD NOT GET TO OUR DEST IF LEFT ON THE EXTREME VECTOR AND THAT WAS WHY I DECLARED THE MINIMUM FUEL. ATC PROMPTLY CLRED US BACK ON COURSE AND I RESCINDED THE MINIMUM FUEL DECLARATION WITH THEM AT THAT TIME. AFTER INCURRING ARR HOLDING; AND EVEN WITH SOME GENEROUS SHORTCUTS TO OUR RTE; WE LANDED WITH FAA RESERVE 4.1 LBS IN ZZZ IN MVFR WX. OUR CLRNC OUT OF HOLDING WAS RECEIVED AT THE MOMENT WE HAD SET FOR DIVERSION TO ZZZ2. IN RETROSPECT; I BELIEVE I ERRED IN NOT ADDING MORE FUEL FOR THIS FLT. I ALSO MIGHT HAVE USED LESS DRACONIAN LANGUAGE FOR OUR FUEL SITUATION WITH ATC THOUGH I BELIEVE I COMPLIED WITH THE SPIRIT AND LETTER OF THE FOM IN DECLARING MINIMUM FUEL ONCE WE WERE BEING DELAYED ENRTE. I AM SURE ATC EXPECTS THE MINIMUM FUEL DECLARATION TO BE USED MORE COMMONLY WHEN APCHING THE DEST ARPT BUT STILL FEEL WHAT I DID WAS PROBABLY NECESSARY TO CONVEY OUR FUEL SITUATION TO ATC WHEN THEY THREW VERY UNEXPECTED AND EXTREME DELAYING TACTICS AT US.