Reproducibility of repeated crystallization experiments from melts is obtained after annealing the melt at a sufficiently high temperature for short time, or at lower temperatures for longer time. This annealing process erases the polymer melt memory. Its physical origin remains elusive, but it is linked to precursor structures for crystallization. What precursor structures are, and how they are affected by shear flow and melt temperature is also unclear. We identify in this work two well-defined melt states: the fully relaxed melt and the melt sheared up to a steady state. Crystallization from fully relaxed melts is slowest while from melts sheared up to the steady state is fastest. We demonstrate that polymers crystallized at the same temperature from the two different melt states have similar average spherulite size, but melts sheared up to steady state have lower viscosity and low number of entanglements, this being the reason for the acceleration of crystallization kinetics in these melts. Annealing of the melts sheared up to the steady state slows down the crystallization kinetics until it becomes comparable with that of fully relaxed melts. (C) 2010 Elsevier Ltd. All rights reserved.