  We address the issue of fine-tuning of the initial field configuration that
can lead to hybrid inflation in the context of global supersymmetry. This
problem is generated by the difference between the energy scale at which the
Universe emerges from the Planck era and the inflationary scale implied by the
COBE observations: V^{1/4} \sim 10^{-3} m_{Pl}. We propose a scenario with two
stages of inflation. The first stage, with a typical scale not far from m_{Pl},
occurs ``naturally'' and provides the necessary homogeneity for the second
stage. The latter generates the density perturbations that result in the cosmic
microwave background anisotropy observed by COBE.
