Elixir said the Hercules 152 jack-up rig was expected to take 28 days to directionally drill Well-2 to a total depth of 9360 feet from the ‘A' production platform.
The well is targeting several sands containing a combination of proved, probable and possible reserves.
Following the success of Well-1, the Pompano JV is now refurbishing both the ‘B' caisson location and the ‘A' production platform using two jack-up workboats.
This operation primarily involves testing the buried pipelines between the ‘B' caisson and the ‘A' production platform, the outcome of which will dictate the timing of first gas from Well-1.
Elixir managing director Andrew Ross said the company was pleased with the progress at Pompano, its first project in the Gulf of Mexico.
"The results achieved from Well-1 have been encouraging, with flow rates during the testing programme exceeding our expectations," Ross said.
"We are looking forward to further success with the second well in the program and to first gas at Pompano, which will add to the company's existing revenue stream from its High Island 268-A production."
Last week, the partners announced that Well-1 was expected to come online at an initial 6-7 million cubic feet of gas per day.
The Pompano Project is essentially a redevelopment of the Pompano gas field with new well locations based on modern 3D seismic data.
The project is about 145km southwest of Houston.
Buccaneer Energy, which listed on the Australian Securities Exchange on November 14, has a 65% stake in the well, while Elixir has 25%. The remainder is held by United States companies.