As shown by time-and temperature dependent SAXS experiments, crystals of s-PP do not change their thickness during isothermal crystallization and a subsequent heating to melting. This allows an accurate determination of the relations between crystallization temperature, crystallite thickness, rate of crystallization, and melting points. There are five main results obtained in a comprehensive SAXS and DSC investigation : (i) Crystals have greatly varying stabilities, in spite of their uniform thickness; the first crystals melt close to the crystallization temperature. (ii) Melting points are affected by the distance to neighboring crystals. (iii) Crystals perfect during heating and annealing. (iv) Recrystallization after melting, as observed for low enough heating rates, starts with crystal growth rates that are at least 2 orders of magnitude higher than for a primary crystallization, and then slows down progressively, being accompanied by an increase in crystal thickness. (v) The dynamic signals observed in a MDSC run are indicative of a smooth change between crystallization and melting at the growth front. Data evaluation yields the average time required for a melting of individual crystallites. A four state scheme allows a description of the behavior. It is based on the following assumptions : (i) Primary crystallization from the melt produces in a first step imperfect "native" crystals, which are subsequently stabilized by structural relaxation processes. These affect both the interior and the surface region. Crystallization proceeds under a small driving force, near to the equilibrium between melt and native crystals. (ii) The amount of structural relaxation is nonuniform thus producing crystals of different stability. (iii) With increasing crystallization temperature, i.e., decreasing growth rate, native crystals continuously approach the equilibrium state. (iv) The main part effusion takes place near the equilibrium between the relaxed crystals and the disentangled melt.