The surface-density profiles of dense filaments, in particular those traced by dust emission, appear to be well fit with Plummer profiles, i.e. Σ(𝑏) = ΣHere Σ B is the background surface-density; Σ B + Σ O is the surface-density on the filament spine; 𝑏 is the impact parameter of the line-of-sight relative to the filament spine; 𝑤 O is the Plummer scalelength (which for fixed 𝑝 is exactly proportional to the full-width at half-maximum,); and 𝑝 is the Plummer exponent (which reflects the slope of the surface-density profile away from the spine). In order to improve signal-to-noise it is standard practice to average the observed surface-densities along a section of the filament, or even along its whole length, before fitting the profile. We show that, if filaments do indeed have intrinsic Plummer profiles with exponent 𝑝 INTRINSIC , but there is a range of 𝑤 O values along the length of the filament (and secondarily a range of Σ B values), the value of the Plummer exponent, 𝑝 FIT , estimated by fitting the averaged profile, may be significantly less than 𝑝 INTRINSIC . The decrease, Δ𝑝 = 𝑝 INTRINSIC − 𝑝 FIT , increases monotonically (i) with increasing 𝑝 INTRINSIC ; (ii) with increasing range of 𝑤 O values; and (iii) if (but only if) there is a finite range of 𝑤 O values, with increasing range of Σ B values. For typical filament parameters the decrease is insignificant if 𝑝 INTRINSIC = 2 (0.05 Δ𝑝 0.10), but for 𝑝 INTRINSIC = 3 it is larger (0.18 Δ𝑝 0.50), and for 𝑝 INTRINSIC = 4 it is substantial (0.50 Δ𝑝 1.15). On its own this effect is probably insufficient to support a value of 𝑝 INTRINSIC much greater than 𝑝 FIT 2, but it could be important in combination with other effects.