  The most general $SU(2)\times U(1)_Y$-symmetric quartic potential with two
Higgs doublets, subject to an only softly broken discrete symmetry
$(\phi_1,\phi_2)\to(-\phi_1,\phi_2)$, is considered. At tree-level, analytic
bounds on the parameters are derived that ensure a stable vacuum, breaking
$SU(2)\times U(1)_Y$ down to $U(1)_{em}$.
