Robust neural encoding of speech in noise is influenced by several factors, including signal-to-noise ratio (SNR), speech intelligibility (SI), and attentional effort (AE). Yet, the interaction and distinct role of these factors remain unclear. In this study, fourteen native English speakers performed selective speech listening tasks at various SNR levels while EEG responses were recorded. Attentional performance was assessed using a repeated word detection task, and attentional effort was inferred from subjects' gaze velocity. Results indicate that both SNR and SI enhance neural tracking of target speech, with distinct effects influenced by the previously overlooked role of attentional effort. Specifically, at high levels of SI, increasing SNR leads to reduced attentional effort, which in turn decreases neural speech tracking. Our findings highlight the importance of differentiating the roles of SNR, SI, and AE in neural speech processing and advance our understanding of how noisy speech is processed in the auditory pathway.