AN AIR CARGO B727 HAD TO SHUT DOWN ITS #3 ENG. EMER DECLARED. INFLT ENG SHUTDOWN. ACFT EQUIP PROB OIL FILTER BYPASS.

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ENRTE TO IAH IN A B727 CARGO ACFT. WE WERE CLRED TO 25000 FT. OUT OF ABOUT 19000 FT; THE #3 OIL FILTER BYPASS LIGHT ILLUMINATED. WE PROCEEDED WITH A PRECAUTIONARY ENG #3 SHUTDOWN. WE WERE THEN OUT OF ABOUT 22000 FT. ZHU TOLD US TO DSND IMMEDIATELY TO 20000 FT FOR CONFLICTING TFC AT 21000 FT. WE DSNDED TO 20000 FT AND THEN ZHU CLRED US TO 19000 FT. AT THAT TIME WE DECLARED AN EMER FOR THE ENG SHUTDOWN AND PROCEEDED TO IAH FOR A LNDG. TFC CLRED US BY ABOUT 1000 FT. CONFLICTING TFC WAS AT 21000 FT; WE WERE AT 20000 FT. WE WERE PREOCCUPIED WITH SHUTTING DOWN #3 ENG AND FAILED TO MAINTAIN A GOOD RATE OF CLB BEFORE DECLARING AN EMER. SUPPLEMENTAL INFO FROM ACN 342717: THE POTENTIAL CONFLICT AROSE DUE TO THE 'UNFORTUNATE' TIMING OF OUR ENG MALFUNCTION AND THE SIMULTANEOUS OCCURRENCE OF THE HDOF PROCESS FROM FT WORTH TO HOUSTON. THE FIRST TIME WE TALKED TO HOUSTON WAS TO LET THEM KNOW WE WERE 'WITH' THEM AND THAT WE HAD AN ENG PROB; WHICH WOULD LIKELY RESULT IN SHUTTING DOWN ONE ENG. AS I RECALL; THEIR FIRST CALL TO US WAS TO DSND DUE TO CO-ALT OPPOSITE DIRECTION TFC.