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The combination of bit-interleaved coded modulation and orthogonal frequency-division multiplexing (BICOFDM) forms a powerful coded modulation scheme for transmission over wideband channels. Recently, Moon and Cox presented a new power allocation method to minimize the biterror rate (BER) of BIC-OFDM. It requires the solution of a convex optimization problem and is limited to (complex) binary transmission. Motivated by their work, in this letter we present an alternative power allocation method, which has the advantages of being a linear program and applicable to arbitrary signal constellations. Our approach relies on a BER approximation which becomes tight for asymptotically large signal-to-noise ratios. Simulative evidence shows that the proposed power allocation method achieves a performance very close to that from for the case of quadrature phase-shift keying.