A DC9-41 OVERSHOT ASSIGNED ALT BY 500 FT BECAUSE THE ACFT WAS CLBING TOO FAST IN ZTL; GA; AIRSPACE.

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FO WAS FLYING FROM PNS TO BHM. DURING CLB TO FL270; SEVERAL VECTORS WERE ISSUED BY CTR TO AVOID AN ACTIVE MOA. AT FL260; THE ALT ALERTER 'CHIMED' AND CAPT STATED 'PASSING FL260 FOR FL270.' ABOUT THE SAME TIME; CTR ISSUED A VECTOR TO 'TURN TO 360 DEGS; DIRECT VUZ WHEN ABLE.' TURN WAS INITIATED; THE LORAN WAS PROGRAMMED DIRECT VUZ; CAPT READ THE CRUISE EPR SETTING; MACH NUMBER AND IAS TO FO FROM CRUISE CHARTS. AT THAT TIME; THE ALT ALERTER 'CHIMED' (300 FT HIGH) AT FL273 FO DISENGAGED AUTOPLT AND RETURNED TO FL270. MAX ALT REACHED WAS FL275 AS VERIFIED BY CTR WHO RESPONDED BY SAYING; 'I'M SHOWING FL275; NO PROB; THERE'S NO TFC IN YOUR AREA; DSND AT PLT'S DISCRETION TO FL270' OR; 'I'M SHOWING YOU LEVEL NOW' (ALL IN ONE XMISSION). CONTRIBUTING FACTORS: EVEN THOUGH I WAS WELL RESTED THAT DAY; I'M SURE THE CUMULATIVE EFFECT OF 5 STRAIGHT 'ALL-NIGHT' OPS PLAYED A PART. THIS WAS A LOW PRESSURE FLT: CLR VFR NIGHT; NOT MUCH RADIO CHATTER; AND CREW COORD/ATTENTIVENESS LAPSED ON THE PART OF THE PF. THE FINAL VECTOR TURN; PROGRAMMING THE LORAN; RECEIVING CRUISE EPR SETTINGS; AND THE LEVELOFF WERE ALL BEING DONE IN A SHORT TIME SPAN. UNFORTUNATELY; THE MOST IMPORTANT; LEVELOFF AT ASSIGNED ALT; IS THE ACTION THAT SUFFERED. SUPPLEMENTAL INFO FROM ACN 396700: THIS WAS THE FIRST LEG OF A 2 LEG FLT; THUS WE WERE LIGHT; CLBING AT ABOUT 2000 FPM. AT FL260 THE ALT ALERT CHIME SOUNDED AND PER OUR PROC I STATED 'OUT OF FL260 FOR FL270' TO WHICH THE FO STATED 'ROGER.' AT THIS TIME PER OUR PROCS; I BEGAN TO LOOK UP THE CRUISE FIGURES (PWR SETTINGS) FOR OUR WT; ALT AND TEMP. AT 27300 FT MSL THE ALT CHIME SOUNDED AND I LOOKED UP FROM MY CHARTS AND NOTICED THAT WE WERE STILL CLBING BUT THE FO HAD STARTED TO PUSH THE NOSE OVER. SINCE WE WERE SO LIGHT; HE WAS UNABLE TO ARREST THE CLB TILL WE WERE AT 27500 FT MSL. THE CTR CTLR CALLED US AND SAID HE SHOWED US AT FL275 AND CLRED US TO DSND TO MAINTAIN FL270.