A LATE DSCNT CLRNC LEADS TO A XING RESTR NOT MET.

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ENRTE TO MIA FROM TADPO INTXN TO WEAVR; WE CALCULATED OUR DSCNT TO CROSS WEAVR AT 10000 FT AND 250 KTS. SINCE THE DSCNT RATE WAS AROUND 2000 FPM; WE REQUESTED LOWER RIGHT AWAY. HOWEVER; MIA WOULD NOT LET US UNTIL A 3000 FPM RATE WAS NEEDED TO MAKE THE XING. NOT ONLY WAS THIS VERY UNCOMFORTABLE TO OUR PAX; BUT THE RESTRS ON OUR SPD BRAKE AND THE CLEAN WING OF THE B737 MAKE IT VERY DIFFICULT TO DSND AT 3000 FPM (WITH A TAILWIND) AND SLOW DOWN AT THE SAME TIME. AT OUR DSCNT POINT; WE WERE AT FL390 OVER MARATHON KEY -- ONLY ABOUT 80 NM FROM OUR DEST. CTR DID GIVE US A DELAY VECTOR; HOWEVER; IT WAS NOT ENOUGH DELAY TO MAKE THE XING. WE REQUESTED RELIEF AND THEY TOLD US NOT TO WORRY ABOUT THE SPD -- JUST MAKE THE ALT. WE TRIED TO MAKE THE ALT; BUT THE RAPID DSCNT OVER A SHORT DISTANCE WOULD HAVE EXCEEDED THE ACFT RED LINE. WE ENDED UP OVER WEAVR AT AROUND 11000 FT AND 290 KTS; TRYING TO GET MORE RELIEF ON A CONGESTED ATC FREQ. ZMA HAS GOTTEN ME HIGH AND FAST IN THIS AREA ON SEVERAL OCCASIONS. THEY NEED TO REALIZE THAT THE B737 DOES NOT 'GO DOWN/SLOW DOWN' VERY WELL.