Analysis of volatile organic compounds (VOCs) on human breath has great potential as a non-invasive diagnostic technique. It is, therefore, surprising that no single, standard procedure has evolved for breath sampling. Here we present a novel repeated-cycle isothermal rebreathing method, where one cycle comprises five rebreaths, which could be adopted for breath analysis of VOCs. For demonstration purposes, we present measurements of three common breath VOCs: isoprene, acetone and methanol. Their concentrations measured in breath are shown to increase with number of rebreaths until a plateau value is reached by at least 20 rebreaths. The average ratio of plateau concentration to single mixed expired breath concentration was found to be 1.92 +/- 0.57 for isoprene, 1.25 +/- 0.13 for acetone and 1.12 +/- 0.12 for methanol (mean +/- standard deviation). Measurements from on-line single exhalations are presented which demonstrate a positive slope in the time-dependent expirograms of isoprene and acetone. The slope of the isoprene expirogram is persistently linear and the end-expired concentration of isoprene is highly variable in the same subject depending on the duration of exhalation. End-expired values of acetone are not as sensitive to the length of exhalation, and are the same to within measurement uncertainty for any duration of exhalation for any subject. It is concluded that uncontrolled single on-line exhalations are not suitable for the reliable measurement of isoprene in the breath and that rebreathing can be the basis of an easily tolerated protocol for the reliable collection of breath samples.