I generally use a regular pistol rod from a cleaning kit with the phosphor bronze brush attached. When I do, I clean from the breech.
However, when I use the CZ-supplied nylon bristle brush, I clean from the muzzle, being careful not to allow the wire handle to come into contact with the muzzle. When used from the muzzle end, the brush reverses in the chamber where there is more room for the bristles to "change directions". I also rotate the brush 1/2 turn while I'm changing direction.
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Mike