A hot topic in the research community is the interworking of integrated IP services, defined by the IETF, with ATM, a technology designed for the transport of multimedia traffic. In particular, the IETF recommends the ATM CBR, nrt-VBR, and ABR service classes for the transport of controlled-load service (CLS) over ATM. In this work the first two alternatives are examined and compared, in order to determine which is the most convenient for CLS. The comparison is carried out in terms of QoS and amount of buffering required at the IP/ATM routers. These performance parameters strongly depend on the parameters of the CLS token bucket shaper, that is, the token bucket depth and token bucket input buffer capacity. A nrt-VBR connection is able to offer a given performance level over a range of values of the token bucket parameters wider than that permitted by a CBR connection. Moreover, in all the examined cases the nrt-VBR connection needs a relatively small ATM buffer at the IP/ATM routers. Since, in order to guarantee acceptable performance, some CLS requests must be rejected, the utilization of the ATM link can be relatively low; this drawback can be overcome by serving the rejected CLS requests as classic best-effort traffic.