In this paper we consider a low cost bit loading based on the greedy power allocation (GPA). Compared to the standard GPA, which is optimal in terms of maximising the data throughput, three suboptimal schemes are suggested, which perform GPA on subsets of subchannels only. We demonstrate how these schemes can reduce complexity. Two of the proposed algorithms can achieve near optimal performance by including a transfer of residual power between subsets at the expense of a very small extra cost. By simulations, we show that the two near optimal schemes perform best in two separate and distinct SNR regions