  We consider a cluster growth model on Z^d, called internal diffusion limited
aggregation (internal DLA). In this model, random walks start at the origin,
one at a time, and stop moving when reaching a site not occupied by previous
walks. It is known that the asymptotic shape of the cluster is spherical. Also,
when dimension is 2 or more, and when the cluster has volume $n^d$, it is known
that fluctuations of the radius are at most of order $n^{1/3}$. We improve this
estimate to $n^{1/(d+1)}$, in dimension 3 or more. In so doing, we introduce a
closely related cluster growth model, that we call the flashing process, whose
fluctuations are controlled easily and accurately. This process is coupled to
internal DLA to yield the desired bound.
  Part of our proof adapts the approach of Lawler, Bramson and Griffeath, on
another space scale, and uses a sharp estimate (written by Blachere in our
Appendix) on the expected time spent by a random walk inside an annulus.
