When delivering intensity modulated treatments the "tongue-and-groove" underdosage effect is a concern that should not be ignored. Algorithms aimed at removing the tongue-and-groove underdosage have been investigated in the past for irradiation of stationary targets. This paper is devoted to algorithms that remove tongue and grove effect for stationary and moving targets. To this end this paper develops original mid-time based algorithms for leaf synchronization. These algorithms exhibit a few additional advantageous properties for DMLC IMRT delivery beyond the removal of tongue-and-grove underdosage. In particular, they safeguard the minimization of time of delivery (for mid-time synchronized algorithms). Moreover, they avoid iterative procedures for synchronization of delivery for multiple pairs of leaves.