Is there a simple construction of a finite solvable group with a given derived length? Given some integer $n$, is there an easy way to construct a finite solvable group of derived length $n$? It would seem that given a solvable group of length $n-1$, one should be able to form the semidirect product with a suitably chosen abelian subgroup of its automorphism group. But I don't see an easy way to ensure that the derived length actually increases this way.

A handy example is provided by the group of $n \times n$ upper triangular unipotent matrices. If $n =2^{t-1}+1$, then its derived length is $t$.