There is strong circumstantial evidence that certain heavy, unstable atomic nuclei are 'octupole deformed', that is, distorted into a pear shape. This contrasts with the more prevalent rugby-ball shape of nuclei with reflection-symmetric, quadrupole deformations. The elusive octupole deformed nuclei are of importance for nuclear structure theory, and also in searches for physics beyond the standard model; any measurable electric-dipole moment (a signature of the latter) is expected to be amplified in such nuclei. Here we determine electric octupole transition strengths (a direct measure of octupole correlations) for short-lived isotopes of radon and radium. Coulomb excitation experiments were performed using accelerated beams of heavy, radioactive ions. Our data on Rn-220 and Ra-224 show clear evidence for stronger octupole deformation in the latter. The results enable discrimination between differing theoretical approaches to octupole correlations, and help to constrain suitable candidates for experimental studies of atomic electric-dipole moments that might reveal extensions to the standard model.