FO OF A GULFSTREAM 4 OVERSHOT DSCNT INTERMEDIATE ALT AFTER VACATING CRUISE ALT DUE TO CLRNC INTERP DISPUTE.

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ENRTE FROM IAH TO ATW AT FL450; THE CAPT (PNF) WENT TO USE THE RESTROOM. SHORTLY THEREAFTER; I RECEIVED CLRNC TO DSND TO FL310. I READ BACK FL310 (I ASSUME) AND DIALED '310' INTO THE ALT PRESELECTOR OR ALERTER; PROGRAMMED THE VERT NAV; AND BEGAN THE DSCNT. AT ABOUT FL404; ZAU RADIOED 'ACFT X; MAINTAIN FL410.' I THEN LEVELED AND CLBED BACK UP TO FL410. AS THE CAPT CLBED BACK INTO THE COCKPIT HE NOTICED A 'TA' ON THE TCASII DISPLAY; BUT I DID NOT NOTICE THIS DISPLAY DURING THE MANEUVER. I THEN RESET THE ALT ALERTER TO FL410 AND CONTINUED THE FLT. I HEARD ZAU CALL OUR POS TO OUR LCL TFC; STATING OUR HORIZ DISTANCE AS 3 MI. NO SAFETY ALERTS WERE ISSUED AND I ASSUME THERE WAS NO CONFLICT. I CANNOT SAY WITH 100% SURETY THAT I READ BACK 'FL310' TO THE CTLR; BUT I DO KNOW WITHOUT A DOUBT THAT I PUT '310' INTO THE ALT ALERTER; AND WHY WOULD I DO THIS IF I WAS NOT TOTALLY CERTAIN THAT WAS MY CLRNC? IT TAKES A LOT OF EFFORT TO CRANK THE ALT ALERTER/PRESELECTOR DOWN FROM 450 TO 310. EXPLANATIONS: CTLR MISTAKENLY CLRED ME TO 'FL310.' CTLR CLRED ME TO 'FL410' AND I READ BACK 'FL310.' CTLR CLRED ME TO 'FL410;' I READ BACK 'FL410' AND DIALED IN 'FL310.' IF I WAS IN ERROR BY PROGRAMMING 'FL310' FOR THE NEXT TARGET ALT; I THINK THIS EVENT WAS THE RESULT OF UNFORTUNATE TIMING SINCE 2 PLTS LISTENING TO ATC RESULT IN FEWER COM ERRORS; AND EXTRA VIGILANCE IS NEEDED WHEN SOMEONE LEAVES THE FLT DECK.