  We prove a new invariant torus theorem, for $\alpha$-Gevrey smooth
Hamiltonian systems, under an arithmetic assumption which we call the
$\alpha$-Bruno-R\"ussmann condition, and which reduces to the classical
Bruno-R\"ussmann condition in the analytic category. Our proof is direct in the
sense that, for analytic Hamiltonians, we avoid the use of complex extensions
and, for non-analytic Hamiltonians, we do not use analytic approximation nor
smoothing operators. Following Bessi, we also show that if a slightly weaker
arithmetic condition is not satisfied, the invariant torus may be destroyed.
Crucial to this work are new functional estimates in the Gevrey class.
