It is shown that polynomial gravity theories with more than four derivatives in each scalar and tensor sectors have a regular weak-field limit, without curvature singularities. This is achieved by proving that in these models the effect of the higher derivatives can be regarded as a complete regularization of the delta-source. We also show how this result implies that a wide class of non-local ghost-free gravities has a regular Newtonian limit too, and discuss the applicability of this approach to the case of weakly non-local models.1 We use the same sign conventions as [10]. Also, we set c = = 1. 2 That is, we shall consider non-local gravity models which are extensions of GR in the UV-limit, which means that for large momentum the propagator decays faster than in GR. Specifically, we require that f 0 (z) and f 2 (z) (defined in (3) and (4)) are constant or diverge at least linearly as z −→ ∞, and that f s (0) = 1. Owed to this improved behaviour in the UV, sometimes these models are called non-local HDG. The situation is quite different from non-local IR modifications of GR, such as those defined by form factors of the type F i ∝ ✷ −1 and F i ∝ ✷ −2 [24-26], or the logarithmic ones, F i ∝ ln ✷, which come from the integration of quantum matter fields in curved space-time [27][28][29][30][31].