Natural-neighbor (n-n) isoseismals are proposed as a new tool that solves the centennial problem of drawing objective and reproducible isoseismals from earthquake damage sparsely observed in a region (felt reports). The algorithm uses the n-n coordinates for weighting, interpolating, and contouring the felt reports. In our computer implementation, at each step, the surface of irregularly distributed observations is partitioned into a unique set of Voronoi polygons computed on a fine regular grid. The interpolation is local, because the weight of an experimental site brought to a new neighbour point is proportional to the area of the intersection of their Voronoi polygons. In the n-n approach, the interpolant (a) fits the data exactly at the observation sites; (b) is isoparametric and bounded by the data values; and (c) is continuously differentiable at all points, except the data sites. Moreover, the n-n isoseismals do not increase the complexity of the quantitative geophysical interpretation because they do not introduce new (contouring) parameters; and, finally, they may be intersected automatically with geological and topographical information. The new natural-neighbor isoseismals appear as a happy compromise between the crude objectivity of the Voronoi tessellation and the intuitive appeal of the somewhat subjective classical isoseismals.