Vanneste competed in the men's singles tournament at the 1992 Summer Olympics.
In 1995, Vanneste entered the finals of the 1995 Wimbledon International but lost to Peter Knowles in two straight games.
[2] He won his first title in men's singles at the 1996 Slovenian International after winning the final against Denis Peshehonov of Ukraine.
[3] He retained his Slovenian International title in 1997 by defeating Boris Kessov in the final.
In 1998, he lost the Slovenian International final to home favorite Andrej Pohar.