  We develop an abstract framework for studying the strong form of Malle's
conjecture for nilpotent groups $G$ in their regular representation. This
framework is then used to prove the strong form of Malle's conjecture for any
nilpotent group $G$ such that all elements of order $p$ are central, where $p$
is the smallest prime divisor of $\# G$.
  We also give an upper bound for any nilpotent group $G$ tight up to
logarithmic factors, and tight up to a constant factor in case all elements of
order $p$ pairwise commute. Finally, we give a new heuristical argument
supporting Malle's conjecture in the case of nilpotent groups in their regular
representation.
