ATX LJ35 FLC ARE QUESTIONED BY SLC SUPVR TO NATURE OF ALT OVERSHOOT.

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I WAS ENRTE FROM APA TO SLC. I WAS FLYING THE ACFT AS PIC AND THE COPLT WAS HANDLING COMS WITH ATC. WE WERE BEING RADAR-VECTORED BY SLC APCH CTL OFF THE SPANE 3 ARR. WHILE IN THE AREA OF THE FAIRFIELD VOR (FFU); WE WERE INSTRUCTED TO DSND AND MAINTAIN 7000 FT. THE COPLT READ BACK THE 7000 FT INSTRUCTION. WHILE DSNDING THROUGH 17000 FT; ATC GAVE A NEW INSTRUCTION TO MAINTAIN 17000 FT. WE HAD BEEN DSNDING AT APPROX 300 FPM WHEN THE NEW ALT WAS GIVEN. THE ACFT WAS AT 16800 FT WHEN I STOPPED THE DSCNT AND BEGAN THE CLB BACK TO OUR NEW ASSIGNED ALT OF 17000 FT. THERE WAS NO CONCERN IN HIS VOICE NOR DID HE STATE THAT THERE WAS ANY PROB. FROM THAT POINT ON; EACH OF HIS INSTRUCTIONS WERE REPEATED UNTIL WE RECEIVED A HDOF TO THE NEXT CTLR. THE REST OF THE FLT WAS UNEVENTFUL. AFTER WE ARRIVED AT OUR HOTEL AT SLC; I RECEIVED A TELEPHONE CALL FROM AN INDIVIDUAL WHO STATED HE WAS AN AIR TFC CTLR ASSIGNED TO THE SLC APCH CTL. HE ASKED ME ABOUT THE ALTDEV. I INFORMED HIM THAT THERE WAS NO DEV. I ADVISED HIM THAT WE WERE ADVISED TO DSND TO 7000 FT IN THE INITIAL REQUEST. JUST AS WE STARTED TO PASS 17000 FT; WE WERE AGAIN CONTACTED BY THE CTLR AND ADVISED TO MAINTAIN 17000 FT. SINCE WE WERE DSNDING APPROX 300 FPM; WE WERE AT 16800 FT WHEN WE BEGAN THE ASCENT. HE ADVISED THAT HE WOULD HAVE TO LISTEN TO THE TAPE AND CALL ME BACK. HE ALSO SAID THAT THE ALT SHOULD HAVE BEEN 17000 FT AND NOT 7000 FT. APPROX 30 MINS LATER; THE SUPVR FROM THE SLC APCH CTL CALLED AND SAID THEY REVIEWED THE TAPES AND THAT THERE WAS STATIC ON THE RADIO AT BOTH ENDS OF THE CONVERSATION AND THEY COULD NOT DETERMINE IF THE CTLR SAID 17000 FT OR 7000 FT. HOWEVER; HE DID SAY THEY HEARD 7000 FT FROM BOTH THE CTLR'S INITIAL INSTRUCTION AND THE COPLT'S READBACK RESPONSE. HE SAID THAT HE COULD NOT TELL WHAT ALT WE DSNDED TO. HE ADVISED ME THAT IT WOULD BE MY DECISION ON WHAT TO DO. HE ASKED ME AGAIN WHAT ALT I WENT TO BEFORE STARTING THE CLB BACK TO 17000 FT. I ADVISED HIM AGAIN THAT IT WAS 16800 FT. HE SAID; 'THANK YOU; I LOVE YOU. WE WILL CONSIDER THIS JUST A PIREP.' THAT WAS THE END OF THE CONVERSATION. AFTER THE CONVERSATION ENDED; IT WAS MY PERCEPTION THAT THERE WAS AN ERROR AT THE CTLR'S END; SINCE BOTH MYSELF AND THE COPLT HEARD THE 7000 FT INSTRUCTION AND THE SUPVR CONFIRMED THE TAPE STATED THE SAME. IF IT HAD BEEN THE ORIGINAL CTLR'S INTENTION THAT WE DSND TO 17000 FT; UPON THE COPLT'S READBACK; THE CTLR SHOULD HAVE CAUGHT THE DISCREPANCY AND PROVIDED THE INTENDED ALT IMMEDIATELY. A FOCUS ON SLOWER; MORE DISTINCT INSTRUCTIONS; AND READBACKS COULD HAVE PREVENTED THIS OCCURRENCE VERSUS THE QUICK PACED COMS WHICH ARE TYPICAL.