Park officials closed a large area of the Teton Range to the public this week so that hunters could shoot goats by helicopter without endangering people on the ground.
Grand Teton spokeswoman Denise Germann says another attempt could take place in late January or early February.
Mountain goats aren't native to the park and biologists worry the 100 or more goats could spread disease to native bighorn sheep.
The National Park Service has contracted Oregon-based Baker Aircraft to shoot goats with non-lead shotgun or rifle rounds, the Jackson Hole News & Guide reports.