CTLR CLRED MTR ACFT THROUGH AN OCCUPIED ALT RESULTING IN LTSS.

Narrative

AFTER CLRING A MIL MTR X TO FL390; I SAW AN ACR Y AT FL330 AS TFC. I BELIEVED ACR Y TO BE ON FREQ AT THE TIME. I ASKED MTR X TO INCREASE RATE OF CLB TO GET ABOVE THE TFC AND HE ACKNOWLEDGED 'I'LL DO THE BEST I CAN.' I THEN TURNED MTR X R TO ESTABLISH LONGITUDINAL SEPARATION AND TIRED TO TURN ACR Y. ACR Y; HOWEVER; WAS NOT ON FREQ. I IMMEDIATELY BACK-COORDINATED FOR ACR Y TO TURN R AND BE PUT ON MY FREQ. THERE WAS A SLIGHT DELAY IN THE DELIVERY OF MY REQUEST WHICH MAY; OR MAY NOT HAVE CONTRIBUTED TO LOSS OF SEPARATION. SUPPLEMENTAL INFO FROM ACN 216613: ACTION TO SEPARATE ACFT INVOLVED SHOULD HAVE BEEN STARTED SOONER TO PROVIDE PROPER SEPARATION. SUPPLEMENTAL INFO FROM ACN 217016: WHILE IN CRUISE AT FL330; FLYING DIRECT TO ROSEWOOD VOR; ZID GAVE US A 20 DEG TURN TO THE R; FOLLOWED ALMOST IMMEDIATELY BY INSTRUCTIONS TO MAKE A STEEP TURN TO THE R. WHILE IN THE TURN; TCASII 'TA' CAME ON AND THE SCREEN (30 MI RANGE) SHOWED TFC AT 11 O'CLOCK (APPROX 4 MI) AND 200 FT BELOW. WE RECEIVED A TCASII DSCNT COMMAND (1000 FPM); AND DSNDED APPROX 300-400 FT AT WHICH TIME WE WERE CLR OF THE CONFLICT. ZID CHANGED US TO A NEW FREQ WHILE WE WERE IN THE TURN. THE NEW FREQ KEPT US 2-3 MINS AND CHANGED US AGAIN. ATC BECAME RATHER BUSY AT THE TIME AND I DIDN'T DISCUSS WITH THEM THE PARTICULARS OF WHAT HAPPENED. MY SPECULATION IS THAT THERE WAS FAST CLBING ACFT CLBING BENEATH US.