FLC OF A B737-700 DSNDED FROM ASSIGNED ALT DUE TO A MISUNDERSTANDING OF ARTCC CTLR CLRNC.

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CLRNC WAS 'DSND TO CROSS WATERVILLE AT FL290.' WE WERE AT FL370. I READ BACK CLRNC BUT HAD WRONG XMIT BUTTON PUSHED. ATC GAVE CLRNC AGAIN AND I READ IT BACK. DON'T RECALL IF I GOT AN ACKNOWLEDGEMENT OF THE READBACK. I ASKED THE FO TO TAKE THE RADIO (HE WAS PF) AS I HAD MISPLACED AN ITEM AND WANTED TO LOOK FOR IT. WE WERE ON SPEAKER. I HEARD ATC GIVE US CLRNC TO FL330 'DSND NOW TO FL330.' TOLD FO I HAD THE RADIO BACK AND ASKED HIM IF WE WERE CLRED TO FL330; BUT STILL OBLIGATED TO CROSS WATERVILLE AT FL290. HE CONFIRMED THAT. WE ASSUMED THAT SINCE THE CLRNC WAS NOT TO DSND AND MAINTAIN FL330; THE FL290 RESTR WAS STILL VALID. HAVE RECEIVED THIS TYPE OF CLRNC MANY TIMES; AND THIS HAS ALWAYS BEEN THE INTENT. WE LEVELED OFF AT FL330 AND SHORTLY THEREAFTER OR BEGAN DSCNT SO AS TO CROSS WATERVILLE AT FL290. FREQ CONGESTION DID NOT ALLOW ME TO CALL LEAVING FL330 UNTIL ABOUT FL326. WHEN I GOT THROUGH TO THE CTLR; HE SAID 'YOU WERE CLRED TO FL330.' WE STARTED AN IMMEDIATE CLB AND I EXPLAINED TO THE CTLR MY UNDERSTANDING OF THE CLRNC. HE TOLD US TO CONTINUE DSCNT TO FL290. APPARENTLY THERE WAS NO TFC CONFLICT. THERE HAD BEEN XING TFC AT FL310; BUT HE WAS WELL BEHIND US. IN THE FUTURE I WILL NEVER 'ASSUME' AND WILL ALWAYS CONFIRM ANY AMENDED ALT CLRNC.