But there was better news for fellow Australian Stephanie Gilmore, who won her heat to clinch a spot in the five-surfer field next month.

"We're going to Trestles baby," Gilmore posted on Instagram, after also making the surf-off last year in the first edition of the title-deciding format.

Wright came into the 10th stop on this year's tour seventh in the rankings after a tough year where she has essentially missed three events due to COVID-19 and visa issues.

Needing a big result to break into the top five, Wright instead was beaten by American Lakey Peterson in a second-round elimination heat on Wednesday (Thursday AEST).

In a low-scoring contest on the treacherous reef break, Wright needed a 2.90 to stay alive in the tournament when she caught a wave inside the last minute of the contest.

The two-time world champion just missed out on the score she wanted, instead posting a 2.70 to narrowly fall short of Peterson's two-wave score of 6.56 out of 20.

"Caught a break there," Peterson said of Wright's attempt to snatch the heat win.

"I was sure she was going to get it.

"Really happy that one rolled my way."

The win means sixth-ranked Peterson is still a chance of reaching the finals at Lower Trestles in California, with only one place remaining.

Reigning world champion Carissa Moore, France's Johanne Defay, Brazil's Tatiana Weston-Webb and seven-time world champion Gilmore have locked in spots in the finals already.

Peterson will face fifth-ranked Costa Rican Brisa Hennessy in the quarter-finals in a heat that has huge consequences for both surfers.

Australian Isabella Nichols was also knocked out of the event on Wednesday, losing to Weston-Webb.

Gilmore will face American Courtney Conlogue in the last eight.

Tahitian wildcard Vahine Fierro pulled off the shock result of the second round, eliminating world No.2 Defay to set up a quarter-final with top-ranked Moore.

Australian Associated Press