  A remarkably simple result is found for the optimal protocol of drivings for
a general two-level Hamiltonian which transports a given initial state to a
given final state in minimal time. If one of the three possible drivings is
unconstrained in strength the problem is analytically completely solvable. A
surprise arises for a class of states when one driving is bounded by a constant
$c$ and the other drivings are constant. Then, for large $c$, the optimal
driving is of type bang-off-bang and for increasing $c$ one recovers the
unconstrained result. However, for smaller $c$ the optimal driving can suddenly
switch to bang-bang type. It is also shown that for general states one may have
a multistep protocol. The present paper explicitly proves and considerably
extends the author's results contained in Phys. Rev. Lett. {\bf 111}, 260501
(2013).
