To asses stability against 1/f noise, the Low Frequency Instrument (LFI) on-board the Planck mission will acquire data at a rate much higher than the data rate allowed by the science telemetry bandwith of 35.5 Kbps. The data are processed by an on-board pipeline, followed on-ground by a decoding and reconstruction step, to reduce the volume of data to a level compatible with the bandwidth while minimizing the loss of information. This paper illustrates the on-board processing of the scientific data used by Planck/LFI to fit the allowed data-rate, an intrinsecally lossy process which distorts the signal in a manner which depends on a set of five free parameters (Naver, r1, r2, q, Script O) for each of the 44 LFI detectors. The paper quantifies the level of distortion introduced by the on-board processing as a function of these parameters. It describes the method of tuning the on-board processing chain to cope with the limited bandwidth while keeping to a minimum the signal distortion. Tuning is sensitive to the statistics of the signal and has to be constantly adapted during flight. The tuning procedure is based on a optimization algorithm applied to unprocessed and uncompressed raw data provided either by simulations, pre-launch tests or data taken in flight from LFI operating in a special diagnostic acquisition mode. All the needed optimization steps are performed by an automated tool, OCA2, which simulates the on-board processing, explores the space of possible combinations of parameters, and produces a set of statistical indicators, among them: the compression rate Cr and the processing noise epsilonQ. For Planck/LFI it is required that Cr = 2.4 while, as for other systematics, epsilonQ would have to be less than 10% of rms of the instrumental white noise. An analytical model is developed that is able to extract most of the relevant information on the processing errors and the compression rate as a function of the signal statistics and the processing parameters to be tuned. This model will be of interest for the instrument data analysis to asses the level of signal distortion introduced in the data by the on-board processing. The method was applied during ground tests when the instrument was operating in conditions representative of flight. Optimized parameters were obtained and inserted in the on-board processor and the performance has been verified against the requirements with the result that the required data rate of 35.5 Kbps has been achieved while keeping the processing error at a level of 3.8% of the instrumental white noise and well below the target 10% level.