Spread spectrum (SS) or known-host-statistics technique has shown the best performance in terms of both rate of reliable communications and bit error probability at the low watermark-to-noise ratio (WNR) regime. These results were obtained assuming that the host data follows an independent and identically distributed (i.i.d.) Gaussian distribution. However, in some widely used in practical data-hiding transform domains (like wavelet or discrete cosine transform domains) the host statistics have strong non-Gaussian character. Motivated by this stochastic modeling mismatch between the used assumption and the real case, a new set-up of the SS-based data-hiding with Laplacian host is presented for performance enhancement in terms of both bit error probability and achievable rates in additive white Gaussian noise (AWGN) channels based on the parallel splitting of Laplacian source.