You can suppress the PCP airguns as well, and no paperwork (i.e. Class 3) is required! In airgun terminology, the suppressors are called moderators.

I shot in one Field Target event where a guy had a PCP FWB that was moderated. All one would hear was the hammer hitting the valve to release the compressed air, then the pellet hitting the steel target.

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3/4 to 1 1/4 ac pond LMB, SMB, PS, BG, RES, CC, YP, Bardello BG, (RBT & Blue Tilapia - seasonal).