  In the absence of experimental constraints, optimal measurement schemes for
quantum state tomography are well understood. We consider the scenario where
the experimenter doesn't have arbitrary freedom to construct their measurement
set, and may therefore not be able to implement a known optimal scheme. We
introduce a simple procedure for minimizing the uncertainty in the
reconstructed quantum state for an arbitrary tomographic scheme. We do this by
defining a figure of merit based on the equally-weighted variance of the
measurement statistics. This figure of merit is straightforwardly based on the
singular value decomposition of the measurement matrix, making it well-suited
for optimization.
