ACR X CLB THROUGH OCCUPIED ALT HAD LTSS FROM Y. SYS ERROR.

Narrative

A KING AIR Y DEPARTED THE HOUSTON TERMINAL AREA NWBOUND. I CLBED THE ACFT TO FL240; THE KING AIR'S REQUESTED FINAL. I THEN RECEIVED A HDOF ON A DC9. I CLBED X TO FL330 ASSUMING I WOULD HAVE LATERAL SEPARATION WITH THE KING AIR. A FALCON JET CHKED ON AND I CLBED HIM TO FL280 WITH A RESTR TO TOP THE KING AIR. IN LATER TFC SEARCHES; I NOTED THE RATE OF CLB OF THE DC9 AS ACCEPTABLE TO CLR THE KING AIR THAT X WAS OVERTAKING. ON MY NEXT SCAN X WAS 7 MI AND 120 KTS FASTER THAN THE TFC. I ISSUED A 60 DEG L TURN BUT SEPARATION WAS LOST. I ASSUMED I HAD GIVEN X THE SAME RESTR TO TOP THE KING AIR WHEN I HAD ONLY GIVEN IT TO THE FALCON. TFC WAS LIGHT BUT BUILDING; AND THE NUMBER OF FLT PROGRESS STRIPS I HAD RECEIVED DID DISTRACT ME. BETTER STRIP MARKING (PUTTING THE RESTR ON X'S STRIP) AND NOT LETTING THE IMPENDING TFC SIT (STRIPS TO BE POSTED) DISTRACT ME WOULD HAVE PREVENTED THIS OCCURRENCE. A LACK OF EXPERIENCE (3 WKS RADAR) WAS A CONTRIBUTING FACTOR AS I DID NOT HAVE AN ASSISTANT CTLR ON THE SECTOR.