The thickening of polymer lamellae which occurs when a melt-crystallized sample is heated within its melting range has been investigated for the morphologically simple polymer poly(4-methylpentene-1) using transmission electron microscopy following permanganic etching. It is shown that, even for an isothermally crystallized sample, the lamellar melting point varies repetitively and systematically with position in the spherulitic texture, being highest for dominant lamellae then progressively decreasing because, it is suggested, of increasing constraints during crystallization. Two thickening processes have been distinguished experimentally. At the beginning of the melting range, the least stable lamellae melt and, given time, recrystallize at greater thicknesses. However, the usual interpretation of a doubly peaked melting endotherm in terms of original and transformed lamellae is shown to be oversimplified. At a higher annealing temperature, between the two peaks of the melting endotherm, a population of lamellae forms which is never melted yet increases its average thickness in the solid state logarithmically with time by a second process operative for all lamellae.