A DC9-30 FLC LEVELS OFF 1000 FT TOO HIGH FOR THEIR XING RESTR. THE FO PF HAD SET HIS OWN ALT ALERT BASED UPON WHAT HE THOUGHT THE CAPT HAD READ BACK TO ATC. ZNY CTLR CORRECTS THE SIT.

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ZNY TOLD US TO CROSS 5 MI W OF LRP VOR AT 12000 FT. AS IS COMPANY PROC THE FO SET THE ALT ALERTER. HOWEVER; HE SET 13000 FT; NOT 12000 FT AS IT SHOULD HAVE BEEN. THE FO WAS FLYING THE ACFT AS WE LEVELED AT 13000 FT. WHEN WE WERE AT THE 5 DME FIX; ZNY ASKED IF WE WERE LEVEL AT 12000 FT. I STATED NO. THE CTLR GAVE US A TURN TO AVOID TFC AND TOLD US TO DSND TO 12000 FT. WE DID SO IMMEDIATELY; ARRIVING AT 12000 FT AT APPROX 2 DME. WHEN TALKING AFTERWARDS WITH THE FO ABOUT WHAT HAD HAPPENED; HE SAID THAT I HAD READ BACK 13000 FT (NOT 12000 FT) WHEN WE RECEIVED THE CLRNC. I CAN'T HONESTLY REMEMBER WHAT I SAID. THIS PROB COULD HAVE BEEN AVERTED MANY TIMES: 1) FO HEARING THE 12000 FT CLRNC INITIALLY AND NOT RELYING ON WHAT I SAID ON THE READBACK. 2) MORE CARE TAKEN ON MY PART -- IF I DID ACTUALLY SAY 13000 FT AND NOT 12000 FT. 3) WHEN THE FO SET 13000 FT IN THE ALT WINDOW I SHOULD HAVE CAUGHT IT. 4) WHEN WE LEVELED AT 13000 FT; I SHOULD HAVE CAUGHT IT. 5) IF I DID READ 13000 FT; NONE OF US (CAPT; FO; CTLR) CAUGHT IT.