Removal of systematic effects is crucial in present and future CMB experiments mapping large fraction of the sky . Accurate CMB measurements ask for multi-feed array instruments observing the sky with a redundant scanning strategy covering the same sky region on different time scales and with different detectors for a better control of systematic effects . We investigate the capability to suppress 1 / f noise features in Time Ordered Data ( TOD ) by using the destriping technique described in Maino et al . 1999 , under realistic assumptions for crossing condition between different scan circles and sky signal fluctuations on small angular scales . We perform , as a working case , Planck -LFI simulated observations with few arcminutes pixel size convolved with LFI beam resolutions . In the noiseless case for crossing condition based on pixels with side larger than the input one , the destriping algorithm inserts extra-noise in the final map of the order of \sim \mu K in rms and few \mu K in peak-to-peak amplitude at 30 GHz . However including instrumental noise ( white and 1 / f noise ) in the TOD , the impact of the sky signal on the destriping is found to be very small . In addition , for crossing condition based on pixels with side half of the one of the final map ( typically \sim 1/3 of the FWHM ) , we find only a small improvement ( \sim 1 % level ) in the destriping quality with respect to the case when crossings are searched on pixels with same size of the final map one . We can conclude that the receiver noise is the driver for destriping quality . We extend the analysis to high values of the knee frequency and find that , although significantly suppressed by destriping , the residual additional noise rms is \sim 31 % larger than the pure white noise rms at f _ { k } = 1 Hz which could be a critical issue in the extraction of CMB angular power spectrum . We verified that the approximation of the 1 / f noise on averaged scan circles as a single baseline still works well even for these high values of the knee frequency . Furthermore , by comparing simulations with different noise levels and different sampling rates , we find that the destriping quality does not significantly depend on the receiver sensitivity whereas it improves proportionally to the improvement of sampling rate . Therefore given a noise level , the higher the sampling rate , the better the destriping quality . This paper is based upon Planck -LFI activities .