We determine the smallest nontrivial blocking sets with respect to t-spaces in PG(n, 2), n >= 3. For t = n - 1, they are skeletons of solids in PG(n, 2); for 1 <= t < n - 1, they are cones with vertex an (n - t - 3)space pi(n-t-3) and base the set of points on the edges of a tetrahedron in a solid skew to pi(n-t-3) (c) 2005 Elsevier Inc. All rights reserved.