  The statistics of burst avalanche sizes $n$ during failure processes in a
fiber bundle follows a power law, $D(n)\sim n^{-\xi}$, for large avalanches.
The exponent $\xi$ depends upon how the avalanches are provoked. While it is
known that when the load on the bundle is increased in a continuous manner, the
exponent takes the value $\xi=5/2$, we show that when the external load is
increased in discrete and not too small steps, the exponent value $\xi=3$ is
relevant. Our analytic treatment applies to bundles with a general probability
distribution of the breakdown thresholds for the individual fibers. The
pre-asymptotic size distribution of avalanches is also considered.
