HS-125 FLT CREW ON A NON PRECISION APCH TO EGE; THEIR SECOND ALTERNATE; HAS AN ALTDEV.

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TRIP DEST WAS ASE. APCHING DBL; WE DETERMINED ASE WAS BELOW MINIMUMS AND RIL; OUR FIRST ALTERNATE; WAS ALSO BELOW MINIMUMS. WE CHOSE EGE AS OUR NEW DEST BECAUSE OF ITS GOOD WX. WE TOOK DELAYING VECTORS TO LOAD THE APCH. BOTH PLTS EXPRESSED CONFUSION AT WHAT APCHS THE FMS DATABASE WAS OFFERING; OUR APCH WAS NOT LISTED (DUE TO BEING A CIRCLE TO LAND APCH). FOR SITUATIONAL AWARENESS REASONS WE DECIDED TO BUILD THE APCH IN THE FMS AND NAV USING RAW DATA. AT THIS POINT THE CTLR BEGAN TURNING US BACK TOWARDS THE IAF AND WE BEGAN TO REVIEW WHAT HAD BEEN ENTERED. LOOKING BACK; IT IS AT THIS POINT THAT WE SHOULD HAVE DISCONTINUED OUR APCH DUE TO FEELING RUSHED. IN OUR HASTE WE BOTH FAILED TO REALIZE THAT THE ALTS WERE ENTERED AT THE WRONG FIXES ON OUR 'BUILT' APCH. XING THE IAF; I CALLED FOR THE NEXT ALT AS INDICATED BY THE FMS AND DSNDED. REACHING THE NEW ALT THE CTLR QUERIED OUR ALT; WHICH WE INDICATED WAS 13000 FT. HE INFORMED US WE SHOULD BE AT 14000 FT FOR THAT SEGMENT OF THE APCH. WE IMMEDIATELY CLBED BACK TO 14000 FT AND FINISHED THE APCH WITH NO FURTHER INCIDENT. THE CTLR DID US AN OUTSTANDING SVC. SEVERAL FACTORS CONTRIBUTED TO THIS DEV: 1) I HAD LESS THAN 5 HRS SLEEP AND AN 0300 WAKE-UP. THIS WAS THE 4TH LEG OF THE DAY AFTER 12 HRS OF BEING AWAKE. FATIGUE WAS AN ISSUE; ESPECIALLY IN REGARDS TO OUR CONFUSION WITH THE FMS. 2) WE DID NOT KNOW OUR ULTIMATE DEST UNTIL THE LAST MIN WHICH CAUSED US TO RUSH AND FEEL RUSHED. 3) WE ALLOWED THE CTLR TO TURN US ONTO THE APCH BEFORE WE WERE READY. AGAIN; WE ALLOWED OURSELVES TO BE RUSHED EVEN THOUGH WE HAD PLENTY OF FUEL AND OPTIONS. HAD WE SIMPLY SLOWED DOWN; ENTERED A HOLD AND REVIEWED THE APCH AS WE NORMALLY WOULD THIS EVENT WOULD NOT HAVE OCCURRED.