AN AT72 CREW; DURING CLBOUT OF ST THOMAS (TIST); OVERSHOT THEIR ASSIGNED ALT.

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WE WERE GIVEN AN INITIAL ALT AFTER TKOF OF 3000 FT MSL. AFTER TKOF FROM RWY 10; THE TWR CALLED TFC ENTERING A R DOWNWIND FOR RWY 10 WHICH WE CALLED IN SIGHT. WE WERE INSTRUCTED TO MAINTAIN VISUAL SEPARATION AND TURN R 250 DEGS. THE CAPT AND I DECIDED THE BEST METHOD OF SEPARATION WAS TO CLB AS QUICKLY AS POSSIBLE SINCE THE OTHER TFC WAS DSNDING INTO THE DOWNWIND. I WAS HAND FLYING THE ACFT AND WAS CLBING THE ACFT PRIMARILY ON VISUAL REFS TO MAINTAIN CONTACT WITH TFC. THE CAPT WAS PREOCCUPIED PERFORMING THE CLB CHKLIST WHEN I REALIZED WE WERE AT 3400 FT MSL. AS I PITCHED OVER TO GET BACK DOWN TO 3000 FT MSL; WE WERE GIVEN A CLB TO 6000 FT MSL. ATC MADE NO REF TO OUR ALT EXCURSION. I BELIEVE MY INATTN TO OUR ALT WAS CAUSED PRIMARILY BY MY FATIGUE THIS WAS THE THIRD DAY OF A 4-DAY TRIP AND THE FIFTH LEG OF 6 LEGS THAT DAY. THE PREVIOUS NIGHT I HAD SLEPT JUST UNDER 8 HRS AND THE NIGHT PRIOR TO THAT ONLY 6 HRS DUE TO SHORT OVERNIGHTS. THE DAY BEFORE THE INCIDENT I WAS ON DUTY 14 HRS AND THE DAY OF THE INCIDENT I HAD ALREADY BEEN ON DUTY 10 HRS. THE FAA SHOULD REWRITE THE REST RULES IN A WAY THAT PREVENTS FATIGUE FROM ACCUMULATING OVER THE DURATION IF MULTI-DAY TRIPS.