For Garbage Collection (GC) to be a generally accepted means of memory management it is required to prove its efficiency. This paper presents a scheme that guarantees that an incremental Garbage Collector will have completed its collection cycle before the system runs out of memory. Furthermore, it is shown that the work that has to be done by the collector in one incremental step is limited by a small constant depending on the percentage of total memory used by the application program. This result then allows a suitable trade-off between memory demand and GC overhead to be found.