We investigate TRTH tick-by-tick data on three exchanges (Paris, London and Frankfurt) and on a five-year span. A simple algorithm helps the synchronization of the trades and quotes data, enhancing the basic procedure. The analysis of the performance of this algorithm turns out to be a a forensic tool assessing the quality of the database: significant technical changes affecting the exchanges are tracked through the data. Moreover, the choices made when reconstructing order flows have consequences on the quantitative models that are calibrated afterwards on such data. Finally, this order flow reconstruction provides a refined look at the Lee-Ready procedure and its optimal lags. Findings are in line with both financial reasoning and the analysis of an illustrative Poisson model.