SIMILAR CALL SIGN PROB OCCURS WHEN ZSU CTLR USES PARTIAL CALL SIGNS AND A C750 CREW RESPONDS TO ABBREVIATED CALL SIGNS.

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WHILE ENRTE TO TNCN AT FL410; WE WERE HANDED OFF BY NEW YORK RADIO TO ZSU; JUST PRIOR TO KRAFT INTXN. AFTER SOME DIFFICULTY IN CHKING IN WITH SAN JUAN; WE FINALLY MADE RADIO CONTACT AND GAVE OUR FULL CALL SIGN AS 'ACFT X.' ZSU LATER RESPONDED AND ASKED FOR A POS RPT CALLING US (OR WHAT WE ASSUMED WAS US) 'ACFT X.' SEVERAL MINS LATER WE HEARD THE CALL 'ACFT X; DSND PLT'S DISCRETION AND MAINTAIN 11000 FT.' WE RESPONDED TWICE (WITH A QUERY) AS 'ACFT X; PLT'S DISCRETION TO 11000 FT;' AND GOT A ROGER FROM SAN JUAN. SHORTLY AFTER WE WERE GIVEN ANOTHER FREQ TO CONTACT. UPON CHKING IN WE WERE TOLD TO RETURN TO THE PREVIOUS FREQ; WE HAD SWITCHED OVER INCORRECTLY. GOING BACK TO THE FIRST SAN JUAN FREQ; WE WERE INFORMED THAT WE HAD TAKEN ANOTHER ACFT'S CALL SIGN AND INCORRECTLY VACATED OUR INITIAL ALT OF FL410. WE STOPPED THE DSCNT AT FL380. THE PROB AROSE BECAUSE OF SEVERAL REASONS: 1) ONE CTLR WORKING 2 FREQS. 2) CTLR SHORTENING CALL SIGNS (WE HAD SEVERAL ACFT IN THE AREA WITH AN 'XY' AS PART OF THEIR N-NUMBERS). AN EASY WAY TO SOLVE THIS PROB IN THE FUTURE IS TO INSIST THAT OUR FULL CALL SIGN IS USED FOR ALL COMS; EVEN IF AN ATTEMPT IS MADE TO SHORTEN IT BY PLTS OR ATC. WE WERE NOT TOLD OF ANY PROBS WITH THE INCORRECT DSCNT AND THE TCASII SHOWED NO TFC WITHIN 25 MI. NO ACFT NEAR MISS OCCURRED.