If the units building up a three-dimensional lattice have different sizes and/or shapes and are randomly distributed the long-range order of the point lattice is destroyed. The integral widths δb of the Debye–Scherrer lines increase quadratically with sin θ for a given set of netplanes. Studying the slopes for the reflexions h00, hh0 and hhh one obtains quantitative information on the paracrystalline distortions in the lattice. In the present paper these slopes are calculated for p.c., b.c.c. and f.c.c. lattices and identical coordination statistics with cylindrical symmetry and two fluctuation parameters α,β. The slopes can be conveniently normalized to the fluctuation Δxa of a lattice cell. In a logarithmic Δxaversusβ2/(α2 + β2) plot of all these types of paracrystalline lattices, observed Δxa values of manganese-rich spinels are fitted as well as possible. A body centred paracrystalline lattice is observed with α/β = 0.7 ± 0.1. This example may illustrate how to analyse reasonably paracrystalline lattices.