Irregular LDPC codes can have capacity-approaching performance with an iterative BP decoder under AWGN channel with BPSK modulation. Generally in BPSK modulation, every bit within the block has the same power. In this paper, we investigate unequal power allocation (UPA) using BPSK modulation for irregular binary LDPC codes. We show that constant power modulation need not lead to the best performance. With UPA we see gains of up to 0.25dB, with larger gains possible if the receiver knows the details of the UPA scheme. Optimal power allocation is shown to depend strongly on the codes in use. Our work demonstrates the promise of the UPA scheme for some irregular LDPC codes.