The surface-density profiles (SDPs) of dense filaments, in particular those traced by dust emission, appear to be well fit with Plummer profiles, i.e. Σ(b) = Σ_B + Σ_O{1 + [b/w_O]²}^{[1 - p]/2}. Here, $\, \Sigma _{{\rm B}}$ 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 scale-length (which for fixed p is exactly proportional to the full width at half-maximum, $w_{{\rm O}}=\rm{\small fwhm}/2\lbrace 2^{2/[p-1]}-1\rbrace ^{1/2}$); and $\, p$ is the Plummer exponent (which reflects the slope of the SDP 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.