20 or 17 cal rods work best with my CZ and Anschutz the others are fine with 22cal rods I have. Pro shot and Brownells have 22rf brushes which are A little smaller then CF 22cal brush if you have A tighter bore rifle. The patch out bore cleaners will not get lead out of your barrels.
This. On the CZ website they actually recommend a .20 rod (to clear the ejector) I use a .17/.20 rod and a .20 jag to clean all my .22s. When a brush is needed, either a dedicated .22 rimfire brush or a .22 pistol brush. For some unknown reason it seems that all manufacturers of cleaning gear make jags and patches too big, especially in the smaller calibers. I also like Rimfire Blend.
A decent cheap cleaning rod if your barrel isn't too long is the Outers coated steel .17 rod which Walmart sells for as little as around $5. I make or modify a lot of my own cleaning gear, including .17/.22 adapters so I can use a conventional 8-32 threaded brush with a .17 rod. I'm pretty sure Brownell's sell the adapters too. I can make two pistol rods by cutting one of the Outers rods into two pieces.
Paul
