  In this paper, we discuss how windows in Euclidean time can be used to
isolate the origin of potential conflicts between evaluations of the
hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic
moment of the muon in lattice QCD and from $e^+e^-\to\text{hadrons}$
cross-section data. We provide phenomenological comparison numbers evaluated
from $e^+e^-\to\text{hadrons}$ data for the window quantities most commonly
studied in lattice QCD, complete with the correlations among them. We discuss
and evaluate modifications of window parameters that could be useful in
dissecting the energy dependence of tensions in the HVP integral and emphasize
that further optimizations require a precise knowledge of the full covariance
matrix in lattice-QCD calculations as well.
