The lengths of fission tracks in an apatite crystal reflect its thermal history. This article is concerned with the estimation of thermal history parameters from semi-track measurements, i.e. the remaining parts of tracks that have intersected a polished prismatic surface. We present formulae and calculations for semi-tracks corresponding to those for projected tracks given in Laslett et al. (1994). For semi-tracks, the formulae are simpler and the potential information is greater. For thermal histories described by two parameters μ 1 and p, corresponding to the maximum palcotemperature and the timing of uplift and erosion or cooling, we study what parameter values can be estimated with reasonable precision, what sample sizes are necessary, how useful are measurements of angles (in addition to lengths), and how the estimates compare with those from confined tracks and from projected tracks. Qualitatively, the results for semi- tracks mimic those for projected tracks: precise estimates can be obtained when p is large, corresponding to recent cooling, andwhen μ 1 is small, corresponding to a high maximum paleotemperature; and measurement of angles improves the estimate of μ 1 but makes only a small improvement to the estimate of p. Quantitatively, there is a substantial gain in precision from measuring semi-tracks rather than projected tracks.