This paper exploits the asymmetric Gaussian curve and its tangent space for the first time. We develop a new method of uncovering hidden absorption bands. We then use the asymmetrical Gaussian curve to derive a Master Equation to fit two overlapping bands. We then demonstrate the use of the asymmetric Gaussian curve to fit four overlapping Gaussian bands, and show how this is relevant to the olivine family spectral complex at 1 μm. We report which olivine endmember is easiest to fit using an asymmetric curve. The limitations of the asymmetric band fitting method and a critical assessment of three commonly used numerical minimisation methods are also provided.