Elasticity is the defining feature of cloud computing. Performance analysts and adaptive system designers rely on representative benchmarks for evaluating elasticity for cloud applications under realistic reproducible workloads. A key feature of web workloads is burstiness or high variability at fine timescales. In this paper, we explore the innate interaction between fine-scale burstiness and elasticity and quantify the impact from the cloud consumer's perspective. We propose a novel methodology to model workloads with finescale burstiness so that they can resemble the empirical stylized facts of the arrival process. Through an experimental case study, we extract insights about the implications of finescale burstiness for elasticity penalty and adaptive resource scaling. Our findings demonstrate the detrimental effect of fine-scale burstiness on the elasticity of cloud applications.