LOS ANGELES (Reuters) - Britney Spears and ex-husband Kevin Federline have started mediation sessions to hash out an agreement over custody of their two sons and avoid a trial set for August, according to Federline's lawyer.

Federline still wants to maintain sole legal and physical custody of the boys while allowing Spears to be involved in their lives "in a very substantial and meaningful way," Federline's lawyer Mark Vincent Kaplan told the entertainment show E! News (www.eonline.com) on Friday.

Spears, 26, lost custody of Sean Preston, 2/12, and James Jayden, 21 months, in January after two brief hospitalizations for psychiatric evaluation that marked a new low for the former teen pop star after a year of increasingly bizarre behavior.

But Spears has since won credit for turning her life around and this week was given court permission to spend overnight visits with her sons in addition to the two daytime visits per week she already enjoys.

The issue of permanent custody is due to be decided in a family court trial in Los Angeles in August but the divorced couple began mediation talks this week.

"Kevin is seeking to maintain the sole legal and physical custody that he presently has. There's nothing magical about 50-50.," Kaplan told E! News in an interview that is set to air on cable TV channel E! on Friday evening.

"He wants to have an order ... that takes into account a certain stability and structure for the kids ... regardless of whose house they happen to be in at any given moment," Kaplan added.

Kaplan said the mediation had not yet resulted in an agreement that would avoid the August trial. But he said the mood was "comfortable, positive and it was a mood that was consistent with opening at least a great dialogue."

Spears, one of the world's most successful pop stars of the early 2000s, and her former backup dancer Federline, 30, were formally divorced last summer after two years of marriage.

In the past six months, Spears' father Jamie has taken over management of her personal and business affairs and the singer is reportedly working on a new album. She has also been mentioned as a possible Emmy award nominee for two guest appearances on US television sitcom "How I Met Your Mother."