A system for providing spinal cord electrostimulation for pain control in a patient, the system comprising: a programming device (213; 413) configured to: receive information about placement of at least one lead (626; 726; 1010, 1020, 1030, 1040, 1050, 1039, 1040, 1041, 1042, 1043, 1044, 1050; 1110, 1120; 1513; 1710, 1720) in a vicinity of a lateral portion of a spinal cord; identify one or more lateral spinal neural targets based on the information about placement of the at least one lead; and receive a user selection from selectable stimulation modes for stimulating the identified one or more lateral spinal neural targets; and an electrostimulator configured to apply electrostimulation energy to the identified one or more lateral spinal neural targets via the at least one lead in accordance with the user selection from the selectable stimulation modes, wherein the one or more lateral spinal neural targets include at least one of: first lateral spinal neural targets, identified for a first contact group which comprises a plurality of electrode-tissue contacts associated with electrodes on the same lead or two or more different leads, including dorsal column, dorsal rootlets, a dorsal root entry zone, a Lissauer's track, and inhibitory interneurons; second lateral spinal neural targets, identified for a second contact group which comprises a plurality of electrode-tissue contacts associated with electrodes on the same lead or two or more different leads, including one or more midline dorsal roots; or third lateral spinal neural targets, identified for a third contact group which comprises a plurality of electrode-tissue contacts associated with electrodes on the same lead or two or more different leads, including one or more lateral dorsal roots. a programming device (213; 413) configured to: receive information about placement of at least one lead (626; 726; 1010, 1020, 1030, 1040, 1050, 1039, 1040, 1041, 1042, 1043, 1044, 1050; 1110, 1120; 1513; 1710, 1720) in a vicinity of a lateral portion of a spinal cord; identify one or more lateral spinal neural targets based on the information about placement of the at least one lead; and receive a user selection from selectable stimulation modes for stimulating the identified one or more lateral spinal neural targets; and receive information about placement of at least one lead (626; 726; 1010, 1020, 1030, 1040, 1050, 1039, 1040, 1041, 1042, 1043, 1044, 1050; 1110, 1120; 1513; 1710, 1720) in a vicinity of a lateral portion of a spinal cord; identify one or more lateral spinal neural targets based on the information about placement of the at least one lead; and receive a user selection from selectable stimulation modes for stimulating the identified one or more lateral spinal neural targets; and an electrostimulator configured to apply electrostimulation energy to the identified one or more lateral spinal neural targets via the at least one lead in accordance with the user selection from the selectable stimulation modes, wherein the one or more lateral spinal neural targets include at least one of: first lateral spinal neural targets, identified for a first contact group which comprises a plurality of electrode-tissue contacts associated with electrodes on the same lead or two or more different leads, including dorsal column, dorsal rootlets, a dorsal root entry zone, a Lissauer's track, and inhibitory interneurons; second lateral spinal neural targets, identified for a second contact group which comprises a plurality of electrode-tissue contacts associated with electrodes on the same lead or two or more different leads, including one or more midline dorsal roots; or third lateral spinal neural targets, identified for a third contact group which comprises a plurality of electrode-tissue contacts associated with electrodes on the same lead or two or more different leads, including one or more lateral dorsal roots. first lateral spinal neural targets, identified for a first contact group which comprises a plurality of electrode-tissue contacts associated with electrodes on the same lead or two or more different leads, including dorsal column, dorsal rootlets, a dorsal root entry zone, a Lissauer's track, and inhibitory interneurons; second lateral spinal neural targets, identified for a second contact group which comprises a plurality of electrode-tissue contacts associated with electrodes on the same lead or two or more different leads, including one or more midline dorsal roots; or third lateral spinal neural targets, identified for a third contact group which comprises a plurality of electrode-tissue contacts associated with electrodes on the same lead or two or more different leads, including one or more lateral dorsal roots.