ACR LTT ACFT FLC INADVERTENTLY UNDERSHOT ASSIGNED ALT.

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CID TO STL; ACR LTT ACFT WAS CLRED TO FL210 BY ZAU. ALT WAS SET ON ALT ALERTER BY THE CAPT. HOWEVER; WE INADVERTENTLY LEVELED OFF AT FL200 AND DID NOT BECOME AWARE OF OUR MISTAKE UNTIL CHANGING FREQ TO ZKC AND ADVISING OF OUR PRESENT ALT. THE CTR CTLR REPLIED ASKING ABOUT ALT CLRED TO; TO WHICH I REPLIED 'WE'RE CLBING TO FL210.' THE CTLR ACKNOWLEDGED AND WE REACHED ASSIGNED ALT SHORTLY THEREAFTER. NO MENTION OF ANY CONFLICT WAS MADE BY ATC. TIME (ESTIMATED) SPENT AT WRONG ALT WAS 5 MINS OR LESS. THE FOLLOWING FACTORS; I FEEL; CONTRIBUTED TO THIS SITUATION: CREW INATTN DUE TO FATIGUE. CREW GOT OFF DUTY THE PREVIOUS NIGHT AT XX07; CHKING INTO HOTEL AT AROUND XY00. CREW DEPARTED HOTEL AT OZ00 NEXT MORNING. CREW WAS ON 'REQUIRED' REDUCED REST OF NO LESS THAN 8 HRS. HOWEVER; CURRENT FARS CONSIDER TRANSPORTATION TO AND FROM HOTEL PART OF 'REQUIRED REST!' ACTUAL CREW REST WAS MORE ON THE ORDER OF 5 HRS. CREW HAD BEEN ON DUTY FOR 10 HRS 56 MINS ON PREVIOUS DAY; FLYING A TOTAL OF 4 HRS 49 MINS.