According to the diffusion model (Ratcliff, 1978), binary decisions stem from a process of continuous evidence accumulation with normally distributed noise. The Lévy-flight model (Voss et al., 2019) extends the diffusion model by the parameter α which further specifies the noise distribution: The lower the value of α, the heavier are the tails of the noise distribution, and the more prevalent are sudden large changes (i.e., jumps) in evidence accumulation. While α can enable a superior fit to the data, its psychological meaning remains empirically underexplored. This study examines whether α reflects guessing, predicting a decrease in α-values as individuals are encouraged to guess. Using a brightness-discrimination task, we employed three conditions that varied in the extent to which guessing was promoted. In the deadline condition, there was a response deadline of 900 ms and instructions stressed accurate responding. In the deadline gut feeling condition, we used the same deadline but instructed participants to follow their gut feeling when in doubt. In the control condition, participants had unlimited time to respond and were instructed to respond as fast and as accurately as possible. As expected, in the presence compared to the absence of a deadline, α-values were significantly smaller. However, the difference in α between the two deadline conditions did not reach statistical significance, likely due to the high difficulty of the employed task alongside the strict deadline. Accordingly, we advocate for and delineate further inquiries of possible interpretations of α, particularly regarding guessing.