The composition of adult mouse aggregation chimaeras is much more variable than X-inactivation mosaics. An early theoretical model proposed that almost all the extra variation in chimaeras arises, before X-inactivation occurs, by spatially constrained, geometrical allocation of inner cell mass (ICM) cells to the epiblast and primitive endoderm (PrE). However, this is inconsistent with more recent embryological evidence. Analysis of published results for chimaeric blastocysts and mid-gestation chimaeras suggested that some variation exists among chimaeric morulae and more variation arises both when morula cells are allocated to the ICM versus the trophectoderm (TE) and when ICM cells are allocated to the epiblast versus the PrE. Computer simulation results were also consistent with the conclusion that stochastic allocation of cells to blastocyst lineages in two steps, without the type of geometrical sampling that was originally proposed, could cause a wide variation in chimaeric epiblast composition. Later allocation events will cause additional variation among both chimaeras and X-inactivation mosaics. We also suggest that previously published U-shaped frequency distributions for chimaeric placenta composition might be explained by how TE cells are allocated to the polar TE and/or the subsequent movement of cells from polar TE to mural TE.