Consider two sets of records from the same survey. One preserves full detail about a few questions under focus (on labour supply), but contains almost no other variables. The other set contains very little information about the question of interest, but has complete information on the remaining variables. Unfortunately, the key that would allow the two sets to be matched is not available. However, the structure of the record sets does allow a partial matahing. In order to extract the maximum amount of information about the question of interest, the use of statistical inference is required. In this paper the EM algorithm, which has been used successfully with censored and incomplete data sets, is adapted to the problem of scrambled data. The performance of the method is assayed using an artificially constructed data set. The relevance of the results for a real world labour market problem is explored.