On the possibility of a very light A^0 at low \tan\beta

The searches at LEP II for the processes e^+e^-\to h^0Z and e^+e^-\to h^0A^0 in the Minimal Supersymmetric Standard Model (MSSM) fail to exclude regions of the m_h,m_A plane where \tan\beta <1, thus allowing a very light A^0 (m_A< 20 GeV). Such a parameter choice would predict a light H^\pm with m_{H^\pm}< m_W. Although the potentially large branching ratio for H^\pm \to A^0 W^* would ensure that H^\pm also escaped detection in direct searches at LEP II and the Tevatron Run I, we show that this elusive parameter space is overwhelmingly disfavoured by electroweak precision measurements.