3G and beyond wideband code division multiple access networks use orthogonal variable spreading factor (OVSF) codes to handle multimedia traffic. OVSF codes suffer from the limitation of code blocking, which leads to new call blocking. Scattered vacant codes in the OVSF code tree are the main cause of code blocking. This study proposes compact single code and multicode assignment schemes to reduce code blocking. The vacant codes used for incoming calls are the ones surrounded by a minimum number of consecutive vacant codes. Furthermore, finding consecutive vacant codes at the leaves of the tree is sufficient to find the consecutive vacant codes for all other layers. Handling non-quantised rates with a single code assignment produces wastage of code capacity, which is avoided with the use of a multicode assignment. Multicode usage facility along with the use of vacant codes from the minimum consecutive vacant code groups results in minimum code blocking. Two categories of the multicode assignment schemes are considered: the first one uses the least number of codes and is suitable for rake limited OVSF system, and the second scheme uses maximum number of codes to reduce code blocking significantly.