FLC OF AN MLG FAILED TO LEVEL OFF DURING SID CLB FOR INTERMEDIATE XING ALT. ATC INTERVENED AND CLRED RPTRS TO A HIGHER ALT AND DID NOT COMMENT ON ALT OVERSHOT.

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DEPARTED RWY 13 AT SJC ON RADAR VECTORS BACK TO THE SJC VOR (R TURN) ON DANVILLE DEP (SID). SID SAYS TO CROSS SJC AT 12000 FT. OUR INITIAL ASSIGNED ALT (FROM PDC) WAS FL230. DURING TURN; BACK TOWARD SJC VOR TOLD TO LEVEL AT I BELIEVE 10000 FT. PRIOR TO REACHING; RECLRED TO FL230; CAPT SET FL230 IN MCP WINDOW. THE CAPT AND I BOTH HEARD CROSS SJC AT OR ABOVE 12000 FT TO MAINTAIN FL230. OUT OF ABOUT 13000 FT OR SO RECLRED TO MAINTAIN 15000 FT. WE WERE OVER SJC AT THIS TIME AND PRIOR TO REACHING 15000 FT WERE AGAIN CLRED TO FL230. NOTHING WAS SAID BY ATC ABOUT TFC AND NONE OBSERVED ON TCASII. ATC ALSO SAID NOTHING ABOUT ALTDEV. SUPPLEMENTAL INFO FROM ACN 391170: WE WERE GIVEN THE R TURN BACK TO THE SJC VOR TO CROSS AT 12000 FT AND THEN MAINTAIN FL230. I READ BACK THE CLRNC AND SET 23000 FT IN THE ALT WINDOW. WE HAD 12000 FT SET IN THE FMS AS THE ALT AT SJC. I TURNED BACK DOWN TO THE RADAR CTL PANEL TO SCAN THE CLOUDS AHEAD AS THERE WERE RAIN SHOWERS AROUND US. WHEN I LOOKED BACK AT THE FLT INSTS; I NOTED THAT WE WERE PAST 13000 FT AND HAD NOT YET REACHED THE VOR. I QUESTIONED THE FO ABOUT OUR ATTITUDE AND HE REPLIED THAT THE CLRNC WAS 'AT OR ABOVE 12000 FT.' I TOLD THE FO THAT I BELIEVED WE WERE SUPPOSED TO MAINTAIN 12000 FT UNTIL THE VOR AS DEPICTED ON THE CHART. NORMALLY VNAV WOULD HAVE POWERED BACK TO MAINTAIN 12000 FT BUT I APPARENTLY DID NOT EXECUTE THE COURSE TO THE VOR UNTIL WE HAD PASSED 12000 FT. THAT PLUS MY CONCERN WITH THE WX RADAR AND SETTING 23000 FT IN THE ALT WINDOW; PLUS THE FO'S MISUNDERSTANDING OF THE CLRNC; CAUSED THE DEV. A STRONG CONTRIBUTING FACTOR WAS FATIGUE. WE WERE 3 HRS LATE ARRIVING THE NIGHT BEFORE DUE TO WX AND MECHANICAL DELAYS AND DID NOT LAND IN SJC UNTIL AFTER XX00 LCL TIME. BY THE TIME WE GOT TO THE HOTEL; IT WAS ABOUT XX45 OUR BODY TIME. WE HAD ALSO BEEN VERY LATE THE PREVIOUS 2 NIGHTS; NOT GETTING TO BED UNTIL PAST XY00. I DO NOT THINK WE WOULD HAVE MADE THOSE ERRORS HAD WE HAD DECENT REST PERIODS THE PREVIOUS NIGHTS. WE ALSO HAD A VERY LIGHT PAX LOAD; SO THE ACFT WAS LIGHT AND CLBING FAST.