Beat me to it, Jerry - I was going to suggest a Weihrauch HW77K (in either calibre) with a 3-9x40 scope & H & N pellets.

Mine in 0.177 flavour likes Field Target Trophy - pellet-on-pellet at 35 metres if I do my bit, so quite capable of eliminating such pests.

Added bonus over poisons is that they don't crawl off & die in your roof space or cavity walls, so less chance of nasty niffs & blue bottle infestations due to inaccessible rotting carcass.

Nigel B.