  Destriping methods for constructing maps of the Cosmic Microwave Background
(CMB) anisotropies have been investigated extensively in the literature.
However, their error properties have been studied in less detail. Here we
present an analysis of the effects of destriping errors on CMB power spectrum
estimates for Planck-like scanning strategies. Analytic formulae are derived
for certain simple scanning geometries that can be rescaled to account for
different detector noise. Assuming {Planck-like low-frequency noise, the noise
power spectrum is accurately white at high multipoles (l<50). D estriping
errors, though dominant at lower multipoles, are small in comparison to the
cosmic variance. These results show that simple destriping map-making methods
should be perfectly adequate for the analysis of Planck data and support the
arguments given in an earlier paper in favour of applying a fast hybrid power
spectrum estimator to CMB data with realistic `1/f' noise.
