FATIGUED B767-300 FLT CREW ON APCH TO LAX DETAIL AN UNSTABILIZED APCH FOLLOWED BY A LEVEL OFF BEFORE GLIDE SLOPE INTERCEPT AND A STICK SHAKER EVENT THAT LED TO A GO-AROUND AND A SUBSEQUENT UNEVENTFUL APCH.

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RETURN LEG TO LAX AT APPROX XA45 PDT. ON APCH TO RWY 6L. BOTH CREW MEMBERS SEEMED ADEQUATELY RESTED AT THE BEGINNING OF THE FLT; BUT I KNOW I WAS VERY TIRED TOWARD THE END. ATC GAVE INSTRUCTIONS EARLY TO SLOW TO 250 KTS DUE TO PRECEDING ACFT. FURTHER REDUCTIONS TO 210; 180; AND THEN FINALLY 160 KTS OCCURRED. I KNEW WE WOULD BE HIGH (ABOVE NORMAL DSCNT PATH) DUE TO THESE SLOWER SPDS; BUT FAILED TO ACCURATELY ASSESS HOW HIGH. CLRNC WAS TO DSND AND MAINTAIN 2000 FT UNTIL ESTABLISHED ON THE LOC; CLRED FOR THE ILS RWY 6L. DSNDING THROUGH 3000 FT; PWR WAS IDLE; FLAPS 15 DEGS; SPD BRAKES FULL EXTENDED. I WAS USING FLCH WITH APP ARMED. AT ABOUT 6 MI OUT CAPT CORRECTLY SUGGESTED IT WAS TIME FOR GEAR. I REMEMBER GLANCING AT THE RADAR TO CHK THE PROX OF THE ACFT IN FRONT AND THEN TO OUR FMC TO DETERMINE HOW FAR ABOVE OUR NORMAL PATH WE WERE. NOTICED IT WAS DECREASING (WE WERE CORRECTING AS I WANTED) AND I BELIEVE WE WERE NOW SOMEWHERE BTWN 300 FT AND 400 FT ABOVE THE PLANNED PATH (PER FMC). MY THOUGHT WAS THAT IT WOULD TAKE LESS THAN A MINUTE BEFORE WE WOULD BE ON GLIDEPATH AND THE GS WOULD BE CAPTURED. THOUGH IT SHOULD HAVE BEEN; GOING AROUND WAS NOT SOMETHING I WAS THINKING ABOUT. I WAS PREPARING TO RAISE THE SPD BRAKES AND GO TO FLAPS 20 DEGS. FLAPS 25 DEGS; THEN 30 DEGS WOULD HAVE FOLLOWED AND I EXPECTED TO BE STABILIZED BY 1000 FT. ADMITTEDLY; I WAS NOT MAKING THESE MENTAL CALCULATIONS QUICKLY; IT SEEMED AS THOUGH I WAS A SECOND OR TWO SLOWER THAN NORMAL. THOUGH WE WERE DSNDING TOWARD THE GS; BECAUSE WE WERE ABOVE; THE ACFT WENT INTO ALT HOLD AT 2000 FT. I FAILED TO RECOGNIZE THAT THIS WOULD OCCUR AND FURTHER; DID NOT RECOGNIZE WHY THE ACFT WAS LEVELING OFF QUICKLY ENOUGH. AS I WAS TRYING TO LOWER THE NOSE 3-4 DEGS TO CORRECT TOWARD THE GS; THE SPD DECREASED. WHILE THE CAPT'S CALL FOR GAR WAS NO DOUBT; APPROPRIATE; IT CAUGHT ME BY SURPRISE. I REMEMBER THE RUDE AWAKENING TRYING TO SWITCH FROM EXPEDITING A DSCNT; WHILE TRYING TO CAPTURE GS; TO SEEING OUR ACFT BEGIN TO LEVEL AT 2000 FT AND THE STICK BEGIN TO SHAKE; THEN TO EXECUTING A GAR FROM A LESS THAN FULL CONFIGN WITH SPD BRAKES EXTENDED. THESE TRANSITIONS DID NOT HAPPEN AS SMOOTHLY AS I WOULD HAVE LIKED! WITH THE AUTOPLT STILL ENGAGED; I PRESSED THE TOGA BUTTON AND ENSURED THE THROTTLES MOVED FORWARD. THINKING THAT THIS GA WOULD BE SLIGHTLY DIFFERENT FROM THOSE I PRACTICED IN THE SIMULATOR JUST A WK BEFORE; I CHKED OUT CONFIGN AND SAID FLAPS ARE OK; GEAR UP. CAPT SAYS HE THOUGHT HE HEARD FLAPS UP. AS THE NOSE PITCHED UP; AND THE SPD SLOWED; I AGAIN FOUND MYSELF WONDERING; 'WHY IS IT DOING THIS?' AS I WAS ABOUT TO DISENGAGE THE AUTOPLT AND HAND FLY THE ACFT THE WAY I WANTED IT TO FLY; THE CAPT BEAT ME TO IT BY TAKING THE ACFT. HE LOWERED THE NOSE AND FURTHER INCREASED THRUST. WE ACCELERATED RAPIDLY AND RAISED THE FLAPS. FINALLY NOTICED AND RAISED THE SPD BRAKES AT 250 KTS. WE TOOK A FEW DEEP BREATHS ON DOWNWIND; AND NOW FULLY AWAKE; CAME BACK AROUND FOR A NORMAL APCH AND LNDG. SUPPLEMENTAL INFO FROM ACN 804772: I STATED: IT'S GOING TO TAKE MORE THAN THIS TO GET DOWN. WE'RE HIGH.' THE FO THEN EXTENDED THE S/B. WE PASSED ALISN (6.7 DME) AT ABOUT 2800 FT WITH FLAPS 15 DEGS; I STATED: 'IT'S TIME FOR THE GEAR' AND I REACHED FOR THE GEAR HANDLE; AND THE FO CONCURRED. WITH GEAR DOWN; IN A MATTER OF A FEW SECONDS WE WENT FROM 160 KIAS TO ABOUT 130 KIAS AND SLOWING WITH PITCH INCREASING I CALLED 'AIRSPD;' THEN IMMEDIATELY FELT BUFFET; FOLLOWED BY STICK SHAKER! I CALLED 'GAR!' AND ENSURED THE TOGA BUTTON WAS PRESSED AS I GUARDED THE CTLS WITH MY HAND BEHIND THE THROTTLES WITH MY EYES GLUED TO THE ADI. THE FO CALLED FOR; 'FLAPS;' BUT THEY WERE ABOVE 20; SO I RAISED THE GEAR WITH POSITIVE RATE. THE FO RAISED THE NOSE ABOVE 10 DEGS; SLIGHTLY ABOVE THE V BARS; ON THE GAR (S/B WERE STILL OUT; PERHAPS ADDING TO THE PITCH UP) AND I OFFERED ENCOURAGEMENT TO THE EFFECT OF 'LOWER THE NOSE!' BUT THE ACFT HIT STICK SHAKER A SECOND TIME.