A B727-100 FREIGHTER FLC DSNDED BELOW THEIR ASSIGNED ALT WHILE ATTEMPTING TO VISUALLY ACQUIRE THE ARPT.

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WHILE BEING VECTORED FOR A VISUAL APCH TO RWY 31 AT PEORIA; CREW WAS DIRECTED TO 5000 FT AND CALL THE ARPT WHEN VISUAL. PEORIA ARPT IS DIFFICULT TO SEE UNLESS YOU HAVE BEEN THERE OFTEN. WHILE DSNDING TO ALT; CREW WAS LEANING FORWARD TO TRY AND SPOT THE FIELD. IN THE TRANSITION FROM INSTS TO VISUAL; THE CREW WENT BELOW THE ASSIGNED ALT BY 300 FT. THE FO IMMEDIATELY REQUESTED AND WAS GRANTED CLRNC FOR A VISUAL APCH. NO OTHER ACFT WERE IN THE AREA AND NO CONFLICTS OCCURRED AS A RESULT. CAPT WAS FLYING. CAPT HAD JUST MET MINIMAL LEGAL REST AFTER AN MEM-JFK-BOS-MEM TRIP THAT HAD STARTED AT XA30 THE MORNING BEFORE -- A TRIP THAT WILL BE ILLEGAL SOON DUE TO COMPANY POLICY. THIS WAS THE FIRST FLT FOR THE CREW TOGETHER. ALTHOUGH NO PROBS OCCURRED AS A RESULT OF THE ALTDEV; IT SHOWS THAT THE CAPT WAS DISTR FROM HIS DUTIES BY SIMPLY ALLOWING BOTH HE AND THE CREW TO ABANDON THE INSTS AND GO HEADS UP TO FIND THE RWY. THE CREW DISCUSSED THE EVENT USING THE CRM GUIDE IN THE COMPANY FOM. THE REMAINDER OF THE PAIRING THE CREW WAS ALERT. THIS EVENT IS COMMON I AM SURE; BUT AT THE HRS WE FLY FOR OUR COMPANY IT IS IMPORTANT TO BE ALERT.