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Dark spots in the fleece area are often associated with dark fibres in wool, which limits its competitiveness with other textile fibres. Field data from a sheep experiment in Uruguay revealed an excess number of zeros for dark spots. We compared the performance of four Poisson and zero-inflated Poisson (ZIP) models under four simulation scenarios. All models performed reasonably well under the same scenario for which the data were simulated. The deviance information criterion favoured a Poisson model with residual, while the ZIP model with a residual gave estimates closer to their true values under all simulation scenarios. Both Poisson and ZIP models with an error term at the regression level performed better than their counterparts without such an error. Field data from Corriedale sheep were analysed with Poisson and ZIP models with residuals. Parameter estimates were similar for both models. Although the posterior distribution of the sire variance was skewed due to a small number of rams in the dataset, the median of this variance suggested a scope for genetic selection. The main environmental factor was the age of the sheep at shearing. In summary, age related processes seem to drive the number of dark spots in this breed of sheep.