  With the steadily improving sensitivity afforded by current and future galaxy
surveys, a robust extraction of two-point correlation function measurements may
become increasingly hampered by the presence of astrophysical foregrounds or
observational systematics. The concept of mode projection has been introduced
as a means to remove contaminants for which it is possible to construct a
spatial map reflecting the expected signal contribution. Owing to its
computational efficiency compared to minimum-variance methods, the sub-optimal
pseudo-Cl (PCL) power spectrum estimator is a popular tool for the analysis of
high-resolution data sets. Here, we integrate mode projection into the
framework of PCL power spectrum estimation. In contrast to results obtained
with optimal estimators, we show that the uncorrected projection of template
maps leads to biased power spectra. Based on analytical calculations, we find
exact closed-form expressions for the expectation value of the bias and
demonstrate that they can be recast in a form that allows a numerically
efficient evaluation, preserving the favorable O(l_max^3) time complexity of
PCL estimator algorithms. Using simulated data sets, we assess the scaling of
the bias with various analysis parameters and demonstrate that it can be
reliably removed. We conclude that in combination with mode projection, PCL
estimators allow for a fast and robust computation of power spectra in the
presence of systematic effects -- properties in high demand for the analysis of
ongoing and future large scale structure surveys.
