[en] We show that under certain conditions a simple relationship exists between the elastic scattering of a composite halo nucleus and of its core from a stable target. The coupling of the elastic and projectile excitation channels is crucial to the analysis, which is particularly useful when the ratio of the halo to the core mass is small. In the case of ¹¹Be elastic scattering the cross section relationship is quite well satisfied. For both ¹¹Be and ¹⁹C our analysis reveals a significant sensitivity of elastic scattering data to the halo size and structure. copyright 1997 The American Physical Society