Computational efficiency of vortex particle methods (VPMs) is hindered by the particle count increasing in simulation time. To reduce the number of computational elements, two algorithms are presented that downsample the discretized vorticity field representation in two-dimensional variable-core-size VPMs. The two methods are based on existing schemes of particle merging and regridding, and are adapted to follow a compression parameter set a priori. The effectiveness of the schemes is demonstrated on two benchmark cases of external flow: A stationary Lamb-Oseen vortex and an advecting vortex dipole. In both cases, compression is associated with a drastic reduction in particle count and computation time at a cost of diffusive errors in the vorticity field. Crucially, for gentle compression steps applied at appropriate intervals, the immediate errors in the vorticity field are comparable to reference cases despite great improvements in computational time. To examine the long-term impact of compression on accuracy and performance, it is recommended that repeated compressive steps be tested on more complex cases of bluff-body wakes, with a focus on the impact of downsampling on surface forces.