From 1992 to 1997 she was married to Ilija Lupulesku. After separating from Lupulesku in 1996, she played in Japan for a short while, then moved to the United States. In the US she began using her maiden name, Fazlić, but people kept pronouncing it "phallic". Her then-boyfriend, American player Barney Reed, suggested that she change her last name to "Reed", and she did - although they were never married and are no longer dating. Jasna got married on August 20, 2009 to William H. Rather IV, and changed her last name to Rather.
As of 2009 she is the Head Table Tennis Coach at Texas Wesleyan University. Since the inception of the table tennis program at Texas Wesleyan University, the team has brought back to Texas 38 out of the possible 52 collegiate national titles in team, singles and doubles events.