The statistical power of cross-over trials can be increased by taking ‘baseline’ measurements of the outcome variable at the start of each treatment period. Analysis of covariance (ANCOVA), rather than analysis of change scores, takes best advantage of this. However, ANCOVA can give biased treatment effect estimates in observational studies with true baseline imbalance. While in truth balanced, chance baseline imbalance is possible in individual randomized cross-over studies due to their typically small sample size. Although such chance imbalance does not cause biased estimation on average over repeated trials, this simulation study will aim to confirm the appropriateness of ANCOVA when faced with the analysis of data from an individual trial in which chance baseline imbalance is clearly apparent. Randomized cross-over trials were simulated, varying in sample size and the pattern and strength of correlation between repeated measures. Estimates from ANCOVA, change scores, and post-treatment difference were unbiased on average across each set of simulated data sets. ANCOVA and change scores could use baseline information to improve precision, but change scores could also reduce precision if baseline measures were uninformative. Change scores only were correlated with chance within-subject baseline imbalance. All three estimators could be correlated with chance between-subjects imbalance in the first period baseline measurements, the strongest associations being with the post-treatment difference. Consistent results were obtained from a real data example. In conclusion, ANCOVA took best advantage of baseline measures to improve precision, and avoided bias in the widest set of circumstances with chance imbalance in those baseline measures. Copyright © 2010 John Wiley & Sons, Ltd.