Efficient Radio Resource Allocation (RRA) is of utmost importance for achieving maximum capacity in mobile networks. However, the performance assessment should take into account the main constraints of these networks. This letter presents important enhancements to RRA algorithms proposed in [1]. Prior work [1] ignores some important system constraints such as the impact of inter-cell interference and granularity of frequency allocation blocks. Here we show the performance degradation when these system constraints are assumed on the algorithms in [1] as well as propose some improvements on these algorithms in order to achieve better performance.