  We discuss structure formation in models with a spectator field in
small-field inflation which accommodate a secondary period of inflation. In
such models, subgalactic scale primordial fluctuations can be much suppressed
in comparison to the usual power-law $\Lambda$CDM model while the large scale
fluctuations remain consistent with current observations. We discuss how a
secondary inflationary epoch may give rise to observable features in the small
scale power spectrum and hence be tested by the structures in the Local
Universe.
