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An extension of the engineering return-stroke models for lightning strikes to tall structures that takes into account the presence of possible reflections at the return-stroke wavefront and the presence of an upward-connecting leader is presented. Based on the approach proposed by Shostak et al., closed-form, iterative solutions for the current distribution along the channel, and the strike object are derived. Simulation results for the magnetic fields are compared with experimental waveforms associated with lightning strikes to the CN Tower (553 m). It is shown that taking into account the reflections at the return-stroke wavefront results in better agreement with the fine structure of the magnetic-field waveforms. Moreover, the obtained results are in better agreement with experimental observations, reproducing both the early narrow undershoot and the far-field zero crossing. The results also suggest that the typical double-peak response of the radiated fields from tall structures might be due to the combined effect of upward-connecting leaders and reflections at the return-stroke wavefront.