We discuss numerical construction results of locally optimal spacecraft trajectories with a plane solar sail from Earth's circular orbit into near-Sun space. Both the planar (ecliptic) and three-dimensional cases of sailing are examined. The maximum allowable temperature is taken to be the main restriction. The locally optimal control of sail attitude is chosen for the highest decrease rate of the focal parameter for the spacecraft's osculating orbit. In the three-dimensional case, the requirement for the highest rate of orbital plane rotation is included. Complex schemes of sail attitude control are elaborated to attain various types of near-Sun orbits, as well as trajectories for "falling" onto the Sun. Numerical investigations permit flight time determination to required orbits and to study the evolution of osculating orbits.