Methods and apparatuses are described for optimizing local clock skew, and/or for synthesizing clock trees in an incremental fashion. For optimizing local clock skew, the circuit design can be partitioned into clock skew groups. Next, for each clock skew group, an initial clock tree can be constructed that substantially minimizes worst case clock skew in the clock skew group, and then the initial clock tree can be further optimized by substantially minimizing worst case local clock skew in the clock skew group. For performing incremental clock tree synthesis, a portion of a clock tree in the circuit design can be selected based on a set of modifications to the circuit design. Next, a new clock tree can be determined to replace the selected portion of the clock tree. The circuit design can then be modified by replacing the selected portion of the clock tree with the new clock tree.