We propose new absolute moment based estimating functions for blind source separation purposes. Absolute moments are a computationally simple choice that can also adapt to the skewness of source distributions. They have lower sample variance than cumulants employed in many widely used ICA (Independent Component Analysis) methods. The complete estimating function consists of two parts that are sensitive to peakedness and asymmetry of the distribution, respectively. Expression for optimal weighting between the parts is derived using an efficacy measure. The performance of the proposed contrast and employed efficacy measure are studied in simulations.