Here we studied the quantitative behaviour and cell-to-cell variability of a prototypical eukaryotic cell-fate decision system, the mating pheromone response pathway in yeast. We dissected and measured sources of variation in system output, analysing thousands of individual, genetically identical cells. Only a small proportion of total cell-to-cell variation is caused by random fluctuations in gene transcription and translation during the response ('expression noise'). Instead, variation is dominated by differences in the capacity of individual cells to transmit signals through the pathway ('pathway capacity') and to express proteins from genes ('expression capacity'). Cells with high expression capacity express proteins at a higher rate and increase in volume more rapidly. Our results identify two mechanisms that regulate cell-to-cell variation in pathway capacity. First, the MAP kinase Fus3 suppresses variation at high pheromone levels, while the MAP kinase Kss1 enhances variation at low pheromone levels. Second, pathway capacity and expression capacity are negatively correlated, suggesting a compensatory mechanism that allows cells to respond more precisely to pheromone in the presence of a large variation in expression capacity.