Strapping bike pump to bike without it rattling

Hello everyone, I'm looking for a cheap way to attach a small pump to the frame of my bike. I was wondering if anyone had a cheap solution without needing a mount. Maybe some sort of straps that I can tighten up like a belt so it doesn't rattle.
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I'm thinking of attaching it to the bike frame so I don't need to worry about forgetting it, loosing it or not having a jacket pocket to keep it in. Plus it will be more comfortable. Do you think Velcro straps might work?
Here's how I carry pumps on my bikes:
- MTB: I used to use the bottle-cage mount but it got so muddy it was useless, so now it goes in my hydration backpack. I also carry a CO2 inflator in a saddle bag
- road bike(s): I have a small pump in a water-bottle tool kit, which takes up one of the bottle cages. I also have CO2 in there. I swap the tool kit from bike-to-bike as needed
- gravel bike: the pump goes in my jersey pocket, and has yet to fall out despite being a reasonable size.
How long is your seatpost - room on there? You could look at those Velcro cable tidy straps. But as I said, paint rubbing.
Cannondale Synapse alloy with 'guards for the winter roads
Fuji Altamira 2.7 for the summer roads
Trek 830 Mountain Track frame turned into a gravel bike - for anywhere & everywhere
I've strapped a fatter pump to the top tube, on the top using some rubber hair bobbles I pinched off the mrs: put one around the pump, pull it around the frame them put the end back over the pump. Repeat for the other end.
The rubber under the pump gives a little standoff so it doesn't scratch your frame. You have to pull the rubber things tight to get them all the way round.
I might try elastic bands first though, at least then I won't be able to forget the pump.
https://www.sjscycles.co.uk/pumps/topeak-pump-mounting-bracket-for-pocket-rocket-micro-speed/
or £14.00 from Wiggle which is much more expensive but it does come with a free pump and usually Haribo.
Specialising in Git Daaahns and Cafs. Norvern Munkey/Transplanted Laaandoner.