We report results obtained from a systematic analysis of X-ray lags in a sample of black hole X-ray binaries, with the aim of assessing the presence of reverberation lags and studying their evolution during outburst. We used XMM-Newton and simultaneous Rossi X-ray Timing Explorer (RXTE) observations to obtain broadband energy coverage of both the disk and the hard X-ray Comptonization components. In most cases the detection of reverberation lags is hampered by low levels of variability-power signal-to-noise ratio (typically when the source is in a soft state) and/or short exposure times. The most detailed study was possible for GX 339-4 in the hard state, which allowed us to characterize the evolution of X-ray lags as a function of luminosity in a single source. Over all the sampled frequencies (∼0.05–9 Hz), we observe the hard lags intrinsic to the power-law component, already well known from previous RXTE studies. The XMM-Newton soft X-ray response allows us to detail the disk variability. At low frequencies (long timescales) the disk component always leads the power-law component. On the other hand, a soft reverberation lag (ascribable to thermal reprocessing) is always detected at high frequencies (short timescales). The intrinsic amplitude of the reverberation lag decreases as the source luminosity and the disk fraction increase. This suggests that the distance between the X-ray source and the region of the optically thick disk where reprocessing occurs gradually decreases as GX 339-4 rises in luminosity through the hard state, possibly as a consequence of reduced disk truncation.