According to existing theories of simple decision-making, decisions are initiated by continuously sampling and accumulating perceptual evidence until a threshold value has been reached. Many models, such as the diffusion decision model, assume a noisy accumulation process, described mathematically as a stochastic Wiener process with Gaussian distributed noise. Recently, an alternative account of decision-making has been proposed in the Lévy Flights (LF) model, in which accumulation noise is characterized by a heavy-tailed power-law distribution, controlled by a parameter, α. The LF model produces sudden large “jumps” in evidence ac- cumulation that are not produced by the standard Wiener diffusion model, which some have argued provide better fits to data. It remains unclear, however, whether jumps in evidence accumulation have any real psychological meaning. Here, we investigate the conjecture by Voss et al. (2019) that jumps might reflect sudden shifts in the source of evidence people rely on to make decisions. We reason that if jumps are psychologically real, we should observe systematic reductions in jumps as people become more practiced with a task (i.e., as people converge on a stable decision strategy with experience). We fitted four versions of the LF model to behavioral data from a study by Evans and Brown (2017), using a five-layer deep inference neural network for parameter estimation. The analysis revealed systematic reductions in jumps as a function of practice, such that the LF model more closely approximated the standard Wiener model over time. This trend could not be attributed to other sources of parameter variability, speaking against the possibility of trade-offs with other model parameters. Our analysis suggests that jumps in the LF model might be capturing strategy instability exhibited by relatively inexpe- rienced observers early on in task performance. We conclude that further investigation of a potential psychological interpretation of jumps in evidence accumulation is warranted.