B737 ACR FLC ON DEP CLBOUT OF 2700 FT IS ASSIGNED 3000 FT ON INITIAL CONTACT BY TRACON DEP CTLR. ACR ARRESTS ALT AT 3300 FT AND DSNDS. TFC ISSUED APPARENTLY AT 5 MI; CLBING FROM ANOTHER ARPT. FLC ADVISES DEP CTLR SHOULD HAVE COORDINATED THE LOWER ASSIGNED ALT PRIOR TO DEP WHEN THEY HAD BETTER PLANNING FOR THE ALT CHANGE. CAPT PERCEIVED CTLR TRAINING WAS IN PROGRESS.

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WE WERE CLBING OUT ON THE PORTE 3 DEP OUT OF SFO WITH A CLRNC TO CLB AND MAINTAIN FL230. WE WERE VERY LIGHT AND HAD A CLB RATE IN EXCESS OF 4000 FPM; THE AUTOPLT WAS ENGAGED. AT APPROX 2700 FT MSL DEP CTL TOLD US TO STOP OUR CLB AT 3000 FT. WHILE THE FO CONFIRMED WITH DEP IF THEY REALLY WANTED US TO LEVEL AT 3000 FT; I WAS RESETTING THE ALT SELECTOR. BY THE TIME I HAD DIALED 3000 FT INTO THE WINDOW WE HAD ALREADY REACHED 3000 FT. AT THAT TIME I DISCONNECTED THE AUTOPLT AND AUTOTHROTTLES AND BROUGHT THE PWR BACK TO IDLE. I WAS ABLE TO STOP THE CLB AT 3300 FT AND THEN STARTED TO DSND BACK TO 3000 FT AT THE SAME TIME ATC TOLD US OUR ASSIGNED ALT WAS 3000 FT THE FO TOLD ATC THAT WE WERE AWARE OF THE ALT GIVEN TO US BUT THAT THEY HAD GIVEN US VERY SHORT NOTICE TO LEVEL OFF. I THEN TOLD ATC THAT IT WAS NOT POSSIBLE FOR US TO LEVEL OFF IN 300 FT WHEN WE HAD A CLB RATE OF OVER 4000 FPM. THE BOTTOM LINE -- ATC SIMPLY DID NOT GIVE US ENOUGH NOTICE TO LEVEL OFF GIVEN OUR HIGH CLB RATE. THEY SHOULD HAVE COORDINATED WITH TWR TO HAVE US LEVEL AT 3000 FT IF THERE WAS CONFLICTING TFC IN THE AREA. SUPPLEMENTAL INFO FROM ACN 406366: IT IS VIRTUALLY IMPOSSIBLE TO LEVEL OFF IN THAT SHORT OF TIME WHEN THE ACFT IS EXCEEDING 4000 FPM CLB. IT NOW BECOMES AN ISSUE OF SAFETY FOR THE ACFT AND PAX TO BE ABLE TO STOP THE CLB AND LEVEL OFF WOULD HAVE CAUSED UNDUE STRESS ON THE ACFT AND INDUCED NEGATIVE G LOADS ON THE ACFT. THERE MAY HAVE BEEN TRAINING TAKING PLACE AT BAY TRACON FACILITY THIS DAY. THE CTLR DID POINT OUT TFC AT 12 O'CLOCK POS BUT THIS ACFT WAS AT LEAST 5 MI AWAY.