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Bayesian Markov chain Monte Carlo (MCMC) has become one of the principle methods of performing inference of phylogenetic trees. The MCMC algorithm requires the definition of a transition kernel over the state space, which depends on tree proposal operators. So, the precise form of these operators has a large impact on the computational efficiency of the algorithm. In this paper we investigate the efficiency of different tree proposals specialized on clock-constrained phylogenetic trees. Two new operators are developed and their efficiency is compared to five standard operators. Each of the seven operators is tested individually on three synthetic datasets and eleven real datasets. In addition, the single operators are compared to different mixtures of operators. Results show that our new operators perform better than their standard counterparts, but no operator alone achieved a high efficiency on the full panel of data sets tested. Finally, our new proposed mixture using all operators together provides better performance than current techniques.