In the rod and hole paradox as described by Rindler (1961 Am. J. Phys. 29 365–6) ('length contraction paradox'), a rigid rod moves at high speed over a table towards a hole of the same size. A bystander expects the rod to fall into the hole, but a co-moving observer expects it to pass unhindered over the hole. According to the accepted solution as first described in that paper, the entire rod must fall somewhat into the hole and therefore cannot remain rigid when the hole moves underneath it. We present an improved approach that is based on retardation due to speed of stress propagation, and in which proper stiffness is not affected. After showing how to solve the similar but simpler car and hole paradox, we find with the same approach that the rod as depicted in Rindler's paper will not fall into the hole as was claimed and that it may pass practically unhindered over it.