A tracer plume was created within a thin aquifer by injection for 299 d of two adjacent “sub-plumes” to represent one type of plume heterogeneity encountered in practice. The plume was monitored by snapshot sampling of transects of fully screened wells. The mass injection rate and total mass injected were known. Using all wells in each transect (0.77 m well spacing, 1.4 points/m2 sampling density), the Theissen Polygon Method (TPM) yielded apparently accurate mass discharge (Md) estimates at three transects for 12 snapshots. When applied to hypothetical sparser transects using subsets of the wells with average spacing and sampling density from 1.55 to 5.39 m and 0.70 to 0.20 points/m2, respectively, the TPM accuracy depended on well spacing and location of the wells in the hypothesized transect with respect to the sub-plumes. Potential error was relatively low when the well spacing was less than the widths of the sub-plumes (>0.35 points/m2). Potential error increased for well spacing similar to or greater than the sub-plume widths, or when less than 1% of the plume area was sampled. For low density sampling of laterally heterogeneous plumes, small changes in groundwater flow direction can lead to wide fluctuations in Md estimates by the TPM. However, sampling conducted when flow is known or likely to be in a preferred direction can potentially allow more useful comparisons of Md over multiyear time frames, such as required for performance evaluation of natural attenuation or engineered remediation systems.