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Using essentially our 2011 numerical model of a multi-lymphangion segment of a collecting lymphatic vessel, but augmented by inclusion of a refractory period and definition of a mid lymphangion pressure, we explore the effect of several parameters on the form of pump function curves. Pump function is sensitively dependent on the shape of the passive constitutive relation between lymphangion diameter and transmural pressure. Maximum flow-rate increases with the diameter scale applied to the constitutive relation and decreases with the pressure scale. Both maximum flow-rate and maximum pressure difference which can be overcome increase as the excess of lymphangion chain inlet pressure over external pressure is reduced, until inlet pressure is low enough that lymphangion collapse intervenes. The results are discussed in comparison with findings from biological experiments., Comment: 10 pages, 7 figures, 14 references