We study the effects of a class of features of the potential of slow-roll inflationary models corresponding to a step symmetrically dumped by an even power negative exponential factor, which we call local features. Local-type features differ from other branch-type features considered previously, because the potential is only affected in a limited range of the scalar field value, and they are symmetric with respect to the location of the feature. This type of feature only affects the spectrum and bispectrum in a narrow range of scales which leave the horizon during the time interval corresponding to the modification of the potential. On the contrary branch-type features have effects on all the perturbation modes leaving the horizon when the field value is within the interval defining the branch, introducing for example differences in the power spectrum between large and small scale which are absent in the case of local-type features. The spectrum and bispectrum of primordial curvature perturbations are affected by oscillations around the scale $$k_0$$ exiting the horizon at the time $$\tau _0$$ corresponding to the feature. We also compute the effects of the features on the CMB temperature and polarization spectra, showing the effects of different choices of parameters.