Officers were searching the area near Interstate 20 and Moss Avenue for the remains of Rene Escobar Sanchez on January 7th and 8th.
The search -- which was first called off due to the January 9th rainstorm -- came after Jesus M. Venegas reportedly admitted to police on January 5th that he killed Sanchez.
Venegas, 26, also reportedly indicated that Sanchez's body was in the area of Moss Avenue and Interstate 20.
However, police now say the search has been called off as officers look for a more specific area to investigate.
Sanchez, 36, was last seen in July 2008, and his wife later reported him missing.
Venegas is now charged with first degree murder, possession of drug paraphernalia and several traffic violations.
As of Wednesday evening, Venegas was being held in the Ector County Law Enforcement Center.