Broad absorption lines (BALs) in quasar spectra identify high-velocity outflows that likely exist in all quasars and could play a major role in feedback to galaxy evolution. The variability of BALs can help us understand the structure, evolution and basic physical properties of the outflows. Here we report on our first results from an ongoing BAL monitoring campaign of a sample of 24 luminous quasars at redshifts 1.2 < z < 2.9, focusing on C ivλ1549 BAL variability in two different time intervals: 4–9 months (short term) and 3.8–7.7 yr (long term) in the quasar rest frame. We find that 39 per cent (7/18) of the quasars varied in the short-term data, whereas 65 per cent (15/23) varied in the long-term data, with a larger typical change in strength in the long-term data. The variability occurs typically in only portions of the BAL troughs. The components at higher outflow velocities are more likely to vary than those at lower velocities, and weaker BALs are more likely to vary than stronger BALs. The fractional change in BAL strength correlates inversely with the strength of the BAL feature, but does not correlate with the outflow velocity. Both the short-term and long-term data indicate the same trends. The observed behaviour is most readily understood as a result of the movement of clouds across the continuum source. If the crossing speeds do not exceed the local Keplerian velocity, then the observed short-term variations imply that the absorbers are <6 pc from the central quasar.