Motivated by the Deepwater Horizon oil spill in the Gulf of Mexico and by the effects of the Earth's rotation on the oil distribution in the ocean, we investigate the dynamics of single-phase and multi-phase plumes in a homogeneous rotating environment. We conducted small-scale experiments in the laboratory on salt water and bubble plumes in a rotating tank across a wide range of Rossby numbers. In particular, we focus on the plume behaviour in the near-source region where the plume is dominated by its source conditions and study the effects of the source buoyancy flux, the nozzle radius and the rotation rate of the environment on the plume. We report a novel phenomena in the plume dynamics: after approximately one rotation period, the plume axis tilts laterally and the plume starts to precess in the anticyclonic direction. We discuss how the anticyclonic plume precession depends on the plume source conditions and the implications of the precession for plumes in the oceans.