Growth speed dependence of the primary dendrite spacing distribution, the maximum, the median and the minimum, has been examined in Al-4.1wt% Cu, Pb-2.2wt% Sb and Pb-5.8wt% Sb alloys. History dependence of primary spacings has been studied by examining the spacing distributions after step-increase and step-decrease in the growth speed. The "branching-instability" process that determines the upper limit of the primary spacings is found to be less sluggish as compared with the "submerging process" that determines the lower spacing limit. In the absence of convection the minimum, the median and the maximum spacings show identical growth speed dependence, A(V)(-0.22). Interdendritic convection causes more reduction in the upper limit as compared with the lower limit; and it also reduces the extent of experimentally observed history dependence of the primary spacing. (C) 2003 Elsevier Science B.V. All rights reserved.