Curvelets can represent local plane waves. They efficiently decompose seismic images and possibly imaging operators. We study how curvelets are distorted after demigration followed by migration in a different velocity model. We show that for small local velocity perturbations, the demigration/migration is reduced to a simple morphing of the initial curvelet. The derivation of the expected curvature of the curvelets shows that it is easier to sparsify the demigration/migration operator than the migration operator. An application on a 2D synthetic data set, generated in a smooth heterogeneous velocity model and with a complex reflectivity, demonstrates the usefulness of curvelets to predict what a migrated image would become in a locally different velocity model without the need for remigrating the full input data set. Curvelets are thus well suited to study the sensitivity of a prestack depth-migrated image with respect to the heterogeneous velocity model used for migration.