The explosive growth of molecular sequence data has made it possible to estimate species divergence times under relaxed-clock models using genome-scale datasets with many gene loci. In order both to improve model realism and to best extract information about relative divergence times in the sequence data, it is important to account for the heterogeneity in the evolutionary process across genes or genomic regions. Partitioning is a commonly used approach to achieve those goals. We group sites that have similar evolutionary characteristics into the same partition and those with different characteristics into different partitions, and then use different models or different values of model parameters for different partitions to account for the among-partition heterogeneity. However, how to partition data in practical phylogenetic analysis, and in particular in relaxed-clock dating analysis, is more art than science. Here, we use computer simulation and real data analysis to study the impact of the partition scheme on divergence time estimation. The partition schemes had relatively minor effects on the accuracy of posterior time estimates when the prior assumptions were correct and the clock was not seriously violated, but showed large differences when the clock was seriously violated, when the fossil calibrations were in conflict or incorrect, or when the rate prior was mis-specified. Concatenation produced the widest posterior intervals with the least precision. Use of many partitions increased the precision, as predicted by the infinite-sites theory, but the posterior intervals might fail to include the true ages because of the conflicting fossil calibrations or mis-specified rate priors. We analyzed a dataset of 78 plastid genes from 15 plant species with serious clock violation and showed that time estimates differed significantly among partition schemes, irrespective of the rate drift model used. Multiple and precise fossil calibrations reduced the differences among partition schemes and were important to improving the precision of divergence time estimates. While the use of many partitions is an important approach to reducing the uncertainty in posterior time estimates, we do not recommend its general use for the present, given the limitations of current models of rate drift for partitioned data and the challenges of interpreting the fossil evidence to construct accurate and informative calibrations.