While the events leading up to their recent separation have been anything but discreet, Jesse James and Sandra Bullock's divorce will reportedly likely be a clean split.

"Her legal filing indicates that both she and Jesse are seeking an amicable settlement and that there will be no children at issue in this divorce," Austin-based family attorney Daryl Weinman, who's not involved with the case, told People in a Wednesday report.

"I wouldn't be surprised if this divorce wraps up quietly within two months."

Bullock filed for divorce from the former Jesse James is a Dead Man, Monster Garage and The Celebrity Apprentice star on April 23 in Austin -- where she maintains a home -- and used her backwards initials "B.A.S." on the paperwork, according to People.

"I've never seen anything like that before," Weinman told People. "It's clear that Sandra is seeking as private a divorce as possible."

While Bullock will have no legal rights to James' three children from two previous marriages, she could request visitation from a judge in a separate proceeding or the couple could reach a private visitation agreement, People reported. Bullock has previously stated she plans to remain in their lives.

In addition to announcing the divorce filing on Wednesday, Bullock also revealed that the couple had adopted a newborn son -- Louis Bardo -- in January but had decided to keep it a secret until after the Oscars took place early last month.

Bullock is currently finalizing the adoption as a single parent and a legal expert told People that Louis will not be an issue in the case.

While it remains unclear if the couple has a prenuptial agreement, James will not be entitled to spousal support regardless, Weinman told People, explaining that in Texas a couple must be married a minimum of 10 years for a spouse to qualify for support. James and Bullock wed in July 2005.

Infidelity reports about James first surfaced last month.