HOUSTON — Hess Corp. has signed a long-term lease to occupy all of Discovery Tower, a high-rise office tower under construction at 1501 McKinney St. in downtown Houston. The project, which is being developed by a joint venture between Dallas-based Trammell Crow Co. and Principal Real Estate, has been under construction since March 2008. Given the early stage of construction, the tower is being customized to accommodate Hess Corp. It will rise 29 stories and total 844,763 square feet. Other features, such as floor plate sizes and ceiling heights, are also being customized. The project, which has been renamed Hess Tower, is applying for LEED-Gold certification and, upon receiving the designation, will be the first LEED-Gold office building in Houston’s central business district. Completion is scheduled for summer 2010. Hess Corp. will relocate from its current offices in Houston’s Allen Center to Hess Tower in 2011. Hess Corp. was represented in lease negotiations by Tim Relyea of Cushman & Wakefield. Trammell Crow and Principal were represented by John Pruitt and Cody Armbrister of CB Richard Ellis.