Aims.Understanding the depletion of heavy elements is a fundamental step towards determining the structure of pre-protostellar cores just prior to collapse. We study the dependence of the NO abundance on position in the pre-protostellar cores L1544 and L183. Methods: We observed the 150 GHz and 250 GHz transitions of NO and the 93 GHz transitions of N{2}H+ towards L1544 and L183 using the IRAM 30 m telescope. We compare the variation of the NO column density with position in these objects with the H column density derived from dust emission measurements. Results: We find that NO behaves differently from N{2}H+ and appears to be partially depleted in the high density core of L1544. Other oxygen-containing compounds are also likely to be partially depleted in dense-core nuclei. The principal conclusions are that: the prestellar core L1544 is likely to be "carbon-rich"; the nitrogen chemistry did not reach equilibrium prior to gravitational collapse, and nitrogen is initially (at densities of the order of 104 cm-3) mainly in atomic form; the grain sticking probabilities of atomic C, N and, probably, O are significantly smaller than unity. Appendix A is only available in electronic form at http://www.aanda.org