DWH LCL CTLR ASSUMES PA28 WHICH APPEARS ON BASE LEG FOR RWY 17L IS PREVIOUSLY CLRED IN CLOSED TFC. PA28 CROSSES BOTH FINALS AND COMES IN CONFLICT WITH BE55 ON SHORT FINAL TO RWY 17R; CONTINUING OUT OF CTL ZONE.

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