The deal is that recently my laptop stopped suspending properly. It suspends on closing the lid, but then immediately wakes up. It has Jessie installed since beta, then occasionally upgraded, and it has linux-image-4.9.0-0.bpo.2-amd64 from jessie-backports installed.

Eventually I worked out that apparently it is the xhci_pci module that gets a phantom signal from somewhere, and wakes up the system. I believe the module handles USB transport (esp. 3.0), and it is brought in when I plug in a USB stick.

So, my laptop is sleeping fine until I plug one in, and thereafter it keeps bouncing up, refusing to sleep, until I unload that  module.

Perhaps there's some module option to avoid the misbehaviour. I'll add an edit here if I find something.

EDIT 1: I've realized this to be an age old problem, though ascribed to the xhci_hcd module rather.

EDIT 2: See https://bugzilla.kernel.org/show_bug.cgi?id=66171#c67 which suggests the fix of having

options xhci-hcd quirks=270336

in an /etc/modprobe.d/ file, so as to make the module load with that parameter. I'll try that for a while...