  We introduce a new exponent of simultaneous rational approximation
$\widehat{\lambda}_{\min}(\xi,\eta)$ for pairs of real numbers $\xi,\eta$, in
complement to the classical exponents $\lambda(\xi,\eta)$ of best
approximation, and $\widehat{\lambda}(\xi,\eta)$ of uniform approximation. It
generalizes Fischler's exponent $\beta_0(\xi)$ in the sense that
$\widehat{\lambda}_{\min}(\xi,\xi^2) = 1/\beta_0(\xi)$ whenever
$\lambda(\xi,\xi^2) = 1$. Using parametric geometry of numbers, we provide a
complete description of the set of values taken by
$(\lambda,\widehat{\lambda}_{\min})$ at pairs $(\xi,\eta)$ with $1$, $\xi$,
$\eta$ linearly independent over $\mathbf{Q}$.
