The ACH-tomography is used to image teleseismic travel-time residuals into seismic velocity perturbations beneath a recording network. Commonly, these residuals are determined solely from first arrivals of body-wave phases (e.g., P, PKP, or PKIKP). In this contribution we outline the benefit of adding later phases (e.g., PKKP, SKP, or PcP) to increase the amount of input data and to improve the ray sampling of the target volume. As a case study, a tomographic data set from the Chyulu Hills volcanic field in SE-Kenya, East Africa, is taken. A model (M1) inverted from first arrival residuals is compared with one (M2) based on an extended data set, including 85 later arrival residuals. Model M2 has an improved statistical basis for evaluating the quality of the results. It confirms the principal features of M1, but shows a slightly larger low-velocity anomaly beneath the volcanic field in the uppermost mantle, indicating active magmatic processes.¿ 1997 American Geophysical Union