The radial variation of intensity in reciprocal space is ordinarily the main source of displacement and broadening of powder diffraction profiles, and the usual tangent-plane approximation is adequate for the problem. When the main variation of intensity is perpendicular to the reciprocal radius vector a tangent-paraboloid approximation is necessary. For a layer structure with not too closely spaced random mistakes the centroid displacement of the hk0 reflections is approximately α(2d_hk0σ)^1/2/π², where 2α is the probability of a mistake per unit distance, d_hk0 is the interplanar spacing of the reflection in question and σ is the range over which the profile is measured. The additional variance of the profile under the same conditions is approximately fraction one-thirdσ times the centroid displacement. More complex expressions are given, valid for somewhat larger values of α or smaller values of σ.