I have a troublesome paper shredder that periodically causes my cable
modem to lose its mind, and require a reboot.

Due to physical locations of outlets and cabinet spacing, I have no
choice but to use the same power strip for both shredder and modem.

I suspect conducted but I suppose it could be radiated.

I'd suggest building yourself a filter-box. Use one of the nice
metal-case CLC common-and-differential-mode powerline filter
modules... I usually think of Corcom when I think of these, but
they're made by quite a few companies.

Build it into a large outlet box, along with a fuse (or breaker) and a
line cord. Plug the filter-box into the power strip and plug the
shredder into the filter.

Alternatively, build one right into the shredder - mount it inside the
chassis right where the power cord enters the cabinet, and wire it
into the circuit at this point.

These things can be quite good at snubbing out conducted interference
from noisy motors, etc.

--
Dave Platt AE6EO
Friends of Jade Warrior home page: http://www.radagast.org/jade-warrior
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