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- First WTA tournament: Aix-En-Provence, 18 July 1988
- First opponent: Heike Thoms (GER)
- First win: Coetzer def. Thoms, 6-3, 6-3
- First loss: R16 at Aix-En-Provence, Judith Weisner (AUT) def. Coetzer, 4-6, 6-3, 1-6
- First tournament win: Melbourne, 11 January, 1993
- First final: San Juan, 21 October, 1991
- First semi-final: Phoenix, 11 September 1989
- First win over Top Three player: QF at Boca Raton, 2 March 1992, Coetzer def. Gabriela Sabatini, 4-6, 6-1, 6-2
- First win over no. 1 ranked player: R32 at the Canadian Open, 14 August 1995, Coetzer def. Steffi Graf, 3-6, 6-2, 7-6
- Record against South African opponents: 7/3
- First Grand Slam: French Open, 29 May, 1989
- First Grand Slam win: Coetzer def. Veronika Martinek (GER) 6-4, 6-1
- First Grand Slam loss: Arantxa Sanchez (ESP) def. Coetzer, 3-6, 2-6
- First Grand Slam semi-final: Australian Open, 15 January 1996
- First tie-break played: R32 at Hilton Head, 3 April 1989
- First tie-break won: R32 at Hilton Head, Coetzer def. Mercedes Paz, 7-6, 6-4
- First tie-break lost: R32 at Phoenix, 11 Sept 1989, Coetzer def. Rosalyn Fairbank-Nideffer, 6-1, 6-7, 6-3
- First three-set match played: R16 at Aix-En-Provence, 18 July 1988
- First three-set match won: R32 at Phoenix, 11 Sept 1989, Coetzer def. Rosalyn Fairbank-Nideffer, 6-1, 6-7, 6-3
- First three-set match lost: Weisner def. Coetzer, 4-6, 6-3, 1-6
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Last update: 27/6/98
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