Attachment of downward subsequent dart leaders has been recently proposed as a possible mechanism of lightning damage of wind turbine blades. Since subsequent dart and dart-stepped leaders propagating after the first lightning discharge are one-to-two orders of magnitude faster than downward stepped leaders, the direct evaluation of the dart leader interception by upward connecting leaders from the turbine has not been attempted before. In this paper, the self-consistent leader inception and propagation model SLIM is used to evaluate the lightning attachment process of subsequent dart leaders by accounting the rapid changing electric fields produced by their fast descent toward the ground. For this, an improved evaluation of the charge per unit length required to thermalize the upward connecting leader is derived. The analysis considers upward connecting leaders propagating along the preheated channel of a prior discharge. Three study cases of lightning attachment of dart leaders and dart-stepped leader reported in rocket-triggered lightning experiments are evaluated. It is shown that reasonable predictions of the length, duration, and velocity of positive upward connecting leaders can be obtained with SLIM in agreement with the experimental results. Further research on upward leader discharges necessary to improve the modeling of attachment of dart lightning leaders is discussed.