Systems and computer readable media are described that actuate at least one marine seismic source according to a constrained sequence. The sequence exhibits an actuation time or distance interval between each actuation. The actuation time or distance interval corresponds to the sum of a nominal time or distance and a respective dither time or dither distance for each actuation. The sequence is constrained such that differences between consecutive dither times or dither distances remain within a threshold dither difference. Constraining the sequence according to the threshold dither difference enables increased bottom speeds for the source (i.e., increased speeds of the source relative to the seafloor), while still maintaining at least a minimum actuation time or distance interval for the source, taking into account both the nominal time or distance and the respective dither times or dither differences.