FLT CREW OF A WIDEBODY TRANSPORT ACFT OVERSHOT THE ALT THAT ATC BELIEVED TO BE THE CLEARED ALT. NO TFC CONFLICT OCCURRED AND CLRNC WAS ISSUED TO ANOTHER CRUISE ALT.

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WE WERE OPERATING ENRTE FROM BWI TO ZZZ. WE WERE BEING CTLED BY WASHINGTON ARTCC AND STEP-CLBING TO ALT. WE WERE ON J6 APPROX 90 MI FROM HVQ WHEN THE CTLR CLRED US TO CONTINUE OUR CLB TO FL330. AT THAT POINT WE WERE AROUND FL270. I READ BACK FL330 AND LOOKED AND SAW THE PF HAD DIALED FL330 INTO THE FCP ALT WINDOW WHILE I WAS READING BACK THE CLRNC. WHEN I FINISHED WITH THE ATC READBACK; I VERBALLY CONFIRMED THE SET ALT WITH THE PF PER COMPANY SOP'S. PASSING FL323; ATC CALLED US AND ASKED OUR ALT. I STATED 'PASSING FL323 FOR FL330.' THE CTLR LET US LEVEL AT FL330 AND STATED HE 'THOUGHT' HE CLRED US FOR FL300. I STATED WE THOUGHT HE CLRED US TO FL330. HE THEN ASKED WHAT ALT WE WOULD LIKE AS A FINAL; AND I STATED FL330 WOULD BE FINE. HE GAVE US THE OPTION OF FL320 OR FL340; WE CHOSE FL340 AND HE RECLRED US TO CLB TO FL340. AT FL340 THE CAPT AND I DISCUSSED THE MATTER AND BOTH AGREED WE HEARD FL330 AND THAT I READ BACK FL330. THERE WAS NO TFC CONFLICT CAUSED BY THE ERROR (OURS OR ATC'S -- NOT SURE). WE ALSO NOTED THAT IF OUR CLRNC WAS TO FL300 THE CTLR ALLOWED US TO DEVIATE 2300 FT BEFORE ASKING US OUR ALT. THIS FLT WAS OUR SECOND LEG IN A MORNING OUT AND BACK ZZZ-BWI-ZZZ. WE SHOWED FOR THE TRIP AT XA00. THE CAPT STATED HE HAD GOTTEN ABOUT 4 HRS OF SLEEP BEFORE THE TRIP. I BELIEVE I HAD AROUND THE SAME POSSIBLY LESS. WE WERE DEFINITELY TIRED; AND IF IT WAS OUR MISTAKE FATIGUE WOULD BE A BIG FACTOR. SINCE WE BOTH THOUGHT WE HEARD FL330; I CAN'T THINK OF ANYTHING WE WOULD HAVE DONE DIFFERENTLY; WE FOLLOWED ATC AND COMPANY PROCS. AS I MENTIONED ABOVE; THE CTLR LET US DEVIATE 2300 FT FROM THE ALT HE THOUGHT HE ASSIGNED US BEFORE CALLING TO QUESTION US MAKING ME QUESTION HIS LEVEL OF ALERTNESS. THERE WAS OBVIOUSLY A COM PROB BTWN US THE AIR CREW AND ATC WITH POSSIBLE FATIGUE AND ATTENTIVENESS ISSUES AS FACTORS.