ALTDEV ALT OVERSHOT ON DEP. PROC ACCOUNT WRONG ACARS CLRNC INPUT INTO FMC.

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COPLT PROGRAMMED ACARS AT CLE FOR CLE-ORD REQUESTED A PRE-DEP CLRNC. POSTED PRE-DEP CLRNC; SET ALTIMETER; SQUAWK; AND DEP FREQ. ON DEP UNABLE TO COMMUNICATE WITH DEP CTL. CONTINUED CLB ON 010 DEG HDG TO 7000 FT; TALKED TO TWR AGAIN (ON DEP) AND TOLD THEM UNABLE ON 132.85. THEY SENT US TO A DIFFERENT FREQ FOR DEP CTL. DEP ADVISED US THAT WE WERE GOING THROUGH OUR ASSIGNED ALT OF 5000 FT. WE WERE PASSING 5500 FT GOING TO 7000 FT AS PROGRAMMED ON FMP AND PRE-DEP CLRNC. AFTER LEVELING AT 6000 FT; CTLR ASKED US ABOUT OUR CLRNC. INFORMED HIM OF OUR PRE-DEP CLRNC ONLY TO REALIZE THAT SOMEHOW A PRE-DEP CLRNC FROM THE PREVIOUS LEG WAS BEING FLOWN FROM RDU-CLE. WE FAILED TO CATCH THE MISTAKE AND FLEW AN INCORRECT PRE- DEP CLRNC TO 7000 FT. CREW FATIGUE AND COMPLACENCY ARE CAUSAL. LACK OF ATTN TO DETAIL ALSO; RECOMMEND CLE GND VERIFY PROPER PRE-DEP CLRNC BY READBACK OF PROPER XPONDER CODE IN FUTURE. WE HAD THE RDU-CLE CODE IN XPONDER AT THE TIME. SUPPLEMENTAL INFO FROM ACN 240136: TAKING ANOTHER LOOK AT THE ACARS CLRNC SHOWED WE HAD RECEIVED A CLRNC FOR A FLT RDU-CLE!