Peacock feathers feature a rich gamut of colours, created by a most sophisticated structural colouration mechanism. The feather barbules contain biophotonic structures consisting of two-dimensionally-ordered lattices of cylindrical melanosomes and air channels embedded in keratin. Here, we study the reflectance characteristics of the various peacock tail feather colours by applying bifurcated-probe- and micro-spectrophotometry and imaging scatterometry. We compare the experimental results with published anatomical SEM and TEM data, using a transfer-matrix based effective-medium multilayer model that includes the number and diameter of the melanosome rodlets and air channels, the lattice spacing and the keratin cortex thickness, together with the recently determined wavelength-dependence of the refractive indices of keratin and melanin. Slight variations in the parameter values cause substantial changes in the spectral position and shape of the reflectance bands. We find that the number of layers crucially determines the number of peaks in the reflectance spectra. For a small number of melanosome layers, the reflectance band shape is particularly sensitive to the properties of the uppermost layer, which provides a simple mechanism for tuning the feather colours.