COMMUTER SMA ALT DEVIATION OVERSHOT DURING CLIMB THEN TURNED TRANSPONDER OFF TO TRY AND COVER ERROR.

Narrative

WE TOOK OFF FROM CLE ARPT RWY 36. OUR TKOF CLRNC WAS RWY HDG. OUR PRETAXI CLRNC WAS CLE 6 DEP; MAINTAIN 5000'; EXPECT 9000' 10 MINS AFTER DEP. WE WERE HANDED OVER TO DEP CTL FROM TWR. DEP ASSIGNED 'APPROX' HDG 090 DEGS; MAINTAIN 5000'. I READ BACK CLRNC AND REQUESTED HIGHER. DEP SAID HIGHER WASN'T AVAILABLE YET DUE TO TFC AT 11 O'CLOCK. WE WERE APPROX 4800' AT THIS TIME. CAPT WAS ABOUT TO LEVEL AT 5000' WHEN DEP THEN ASSIGNED HDG 210 DEGS AND CLB TO 6000'. I READ BACK THE CLRNC; TOLD THE CAPT '1000' TO GO;' AND I THEN SET 6000' IN OUR ADF WINDOW (WE SOMETIMES USE THIS AS A MAKESHIFT ALT ALERT; IF ONE ISN'T AVAILABLE). CAPT PROCEEDED TO CLB. I TOLD HIM I'D BE OFF THE FREQ TO TALK TO COMPANY FOR A FEW SECS. WHILE TALKING TO COMPANY; THE CAPT ASKED ME IF WE WERE 'ONLY' CLRD TO 6000'. I CONFIRMED 6000' WAS OUR FINAL FOR NOW. I CHKED BACK IN WITH CAPT AFTER TALKING TO COMPANY. I TOLD HIM I WAS HAVING TROUBLE WITH MY HEADSET. IT WAS CUTTING OUT. ABOUT 30 SECS LATER THE CAPT ASKED; 'WAS OUR ALT ASSIGNED 6000'?' WE WERE ALREADY AT APPROX 6700'. 1 SEC LATER ATC ASKED WHAT OUR ASSIGNED ALT WAS BY DEP CTL. I RESPONDED 6000'. THE CAPT PROCEEDED TO CHANGE SELECTION ON TRANSPONDER FROM 'ALT' TO 'ON'. HE BEGAN DSCNT TO 6000'. THE CTLR SAID HE LOST OUR MODE C AND QUESTIONED OUR ALT. I ASKED THE CAPT; 'DO YOU WANT ME TO TELL HIM THE TRUTH? WHAT SHOULD I SAY?' HE SAID HE'S GOT IT AND ACKNOWLEDGED BEING AT 6000'. BEING AS WE DIDN'T TELL THE TRUTH AND I WASN'T SURE WHAT THE CAPT WAS UP TO; I INDICATED I WASN'T GOING TO TALK TO ATC NOW. AT THIS POINT THE CAPT HANDLED THE REST OF THE RADIO COM BTWN ATC AND US. ATC ASKED US OUR DEST AND ASKED US TO COPY HIS PHONE # AND CALL UPON ARR. THE CAPT COPIED THE # AND ACKNOWLEDGED HE'D CALL WHEN ON THE GND. CONTRIBUTING FACTORS: NO ALT ALERT; DISTR--MY HEADSET CUTTING OUT. FRAME OF MIND--WE STARTED THE DAY EARLY AM; FLEW 1 LEG (35 MINS); SAT ON GND FOR APPROX 7 HRS WAITING FOR ACFT TO COME AVAILABLE; FLT CANCELLED THROUGHOUT DAY DUE TO ACFT AVAILABILITY. I THINK THAT LONG OF A BREAK IN A DAY BREAKS UP YOUR CONCENTRATION. FATIGUE.