The fundamental characteristics of VoIP are constant rate, delay sensitivity, and loss tolerance. VoIP over packet-switched networks including the Internet poses problems because the network service is not guaranteed to meet such requirements, i.e. the available bandwidth as well as the delay and loss bounds. Adaptive rate VoIP is a solution that can mitigate the problem. Adaptive rate VoIP has the ability to adapt its transmission rate to match the available network bandwidth. This helps to reduce or avoid network congestion, which in turn minimizes delay and loss. To implement adaptive rate VoIP, the VoIP source must be able to send packets at different rates. Adaptive multi-rate speech coders are commonly used. However, their voice quality (e.g. MOS) varies depending on the bitrate. In this paper, we propose an alternative of using packetization as a means for rate adaptation while using a constant bitrate coder. We explore how packetization can vary network bandwidth requirement. We then study the effect of packetization on VoIP performance. The simulation study shows an interesting result. Using an optimal packetization can help to improve VoIP performance. At the same time, the amount of voice traffic plays an important role to determine the performance improvement. This study also demonstrates that feasibility of packetization-based adaptive rate VoIP.