  We study the extremes of a class of Gaussian fields with in-built
hierarchical structure. The number of scales in the underlying trees depends on
a parameter alpha in [0,1]: choosing alpha=0 yields the random energy model by
Derrida (REM), whereas alpha=1 corresponds to the branching random walk (BRW).
When the parameter alpha increases, the level of the maximum of the field
decreases smoothly from the REM- to the BRW-value. However, as long as alpha<1
strictly, the limiting extremal process is always Poissonian.
