We investigate a scheduling problem in a TDMA environment where packets may be fragmented. Our model of the problem is derived from a scheduling problem present in data over CATV networks, where a slotted TDMA channel is used to carry both real-time and best-effort traffic. Packets of real-time flows have high priority and are allocated in fixed, periodically located slots. Best-effort packets have lower priority and must therefore use the remaining slots. The scheduling problem tackles the assignment of variable size best-effort packets into the free slots which are left between successive allocation of real-time packets. One of the capabilities of the system is the ability to break a packet into several fragments. But, when a packet is fragmented, extra bits are added to the original packet to enable the reassembly of all the fragments. We transform the scheduling problem into a variant of bin packing where items may be fragmented. When an item is fragmented overhead units are added to the size of every fragment. The overhead associated with fragmentation renders the optimization problem NP-hard; therefore, an approximation algorithm is needed. We define a version of the well-known Next-Fit algorithm, capable of fragmenting items, and investigate its performance. We present both worst case and average case results and compare them to the case where fragmentation is not allowed.