AN MD83 EXPERIENCED #1 ENG COMPRESSOR STALL AT FL330. DSNDED TO 17000 FT AND WAS ABLE TO RECOVER PWR UP TO 1 PT 5 EPR. FLT DIVERTED TO DFW.

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LEVEL AT FL330 ENRTE FROM ZIH TO STL; APPROX 1 HR 30 MINS INTO FLT; WHEN #1 ENG BEGAN COMPRESSOR STALLING. DISENGAGED AUTOTHROTTLE AND REDUCED #1 TO IDLE PWR; STALLS CEASED. ADVANCED PWR ON #1 AND STALLS RETURNED AT 1.2 EPR. RETURNED #1 TO IDLE. NOW CONSIDERED ACFT AS BASICALLY SINGLE ENG AND ASKED MONTEREY FOR LOWER. WITH #2 AT MAX CRUISE AND #1 AT IDLE; DSNDED TO FL230. COULD NOT MAINTAIN SPD AT FL230 SO DSNDED TO 17000 FT. CONTACTED COMPANY MAINT AND DISPATCH DURING THIS TIME FOR HELP. NOW CONSIDERED LNDG AT NEAREST SUITABLE ARPT (MCALLEN OR BROWNSVILLE). COMPANY ASKED IF WE COULD MAKE SAT OR HOU. I CONSIDERED THE ACFT BASICALLY SINGLE ENG AND WANTED TO LAND SOON. FINALLY AGREED WITH COMPANY TO LAND AT CRP. DECLARED AN EMER AND HEADED FOR CRP. WHILE HDG TO CRP WE FOUND THE COMPRESSOR STALL CHKLIST WE HAD BEEN LOOKING FOR AND ACCOMPLISHED THE LIST. WE WERE ABLE TO RECOVER #1 ENG TO 1.5 EPR BEFORE EGT GOT TO CAUTION RANGE. CONTACTED COMPANY DISPATCH AND MAINT AGAIN AND DECIDED IT WOULD BE SAFE TO DIVERT DO DFW (HAD CUSTOMS AVAILABLE AND COMPANY MAINT). RELAYED THIS TO ZHU AND TOLD THEM WE HAD RECOVERED SIGNIFICANT ENG PWR ON #1 AND WERE NO LONGER AN EMER; REQUESTED VECTOR TO DFW. APPROX 45 MINS LATER WE LANDED AT DFW WITHOUT INCIDENT. CRASH EQUIP STOOD BY EVEN THOUGH I HAD TOLD TWR AT DFW THAT WE DIDN'T NEED THEM. SECURED L ENG AFTER LNDG.