Context. Averaged pulse profiles of three nearby pulsars: B1929+10, J0437-4715 and B0950+08 exhibit unusual "double notches". These W-like looking features consist of two adjacent V-shaped dips that approach each other at increasing observation frequency \nu_{\rm obs} roughly at a rate \Delta\propto \nu_{\rm obs} less than or equal to where \Delta is the separation between the notches minima. Aims. We show that basic properties of the notches, namely their W-like look and the rate of their converging can be understood within a narrow class of models of coherent radio emission from pulsars: the free electron maser models based on coherent inverse Compton scattering of parallel oscillations of ambient electric field. Methods. The observed properties of the pulsars imply that the Fourier spectrum of the wiggler-like oscillations is narrow and that the broad-band character of the radio emission reflects the width of the electron energy distribution. Results. Such a model provides a natural explanation for the frequency-independent separation between the main pulse and interpulse of B0950+08 as well as for the lack of radius to frequency mapping in the conal-like emission of J0437- 4715. The frequency behaviour of the main pulse in the profile of the first radio magnetar XTE J1810-197 can also be explained within this model.