The scalability of Internet addressing and routing has been a serious issue and becomes a more urgent problem today because of driving factors like IPv6. A radical impacting element of the scalability is address allocation, as it directly affects routing table structure, hence, IP lookup and routing efficiency. A key problem in IPv4 today is address fragmentation, i.e., one entity is represented by multiple non-contiguous IP address blocks in the routing table. Address fragmentation increases routing table size, therefore degrades scalability. Existing address allocation practices are a major contributor to address fragmentation. In this paper, we demonstrate that the performance of address allocation can be dramatically improved. We propose a new address allocation algorithm called GAP: Growth-based Address Partitioning. Through real data, we show that GAP can reduce fragmentation by 90% compared to the existing allocation schemes. This is significant for reducing routing table size, increasing scalability, and improving the performance of the Internet. We also introduce a software tool being developed for address allocation.