For ages it's bugged me that the New Yorker uses spellings like focussing and travelled, even though the accent is on the first syllable. Now I see they've used combating, which, it seems to me, should have a double-t. Have the rules changed?

Maybe-- or maybe just the editors.. standards at The New Yorker are not what they used to be! (Tina Brown has basing almost became a world class sport-- she is gone, and so are many editors)

That shows you pronounce it com-BAT, and if you did you'd be right to double the T in combatting.

I was going to say the stress on -BAT sounded old-fashioned to me, and British, but it turns out it's the other way round. My old Shorter Oxford has COM-bat and CUM-bat for both noun and verb, with no mention of the -BAT stress. Fowler (Modern English Usage) has only CUM- and mentions it under the -T- vs -TT- rule as one that goes combated etc., so he also pronounced it with unstressed -bat.

A modern dictionary (Chambers) now only has COM-/com- (no-one says cumbat any more), but notes that the -BAT stress is North American, and rare here.

The style-guide advice in Britain would be not to double S or T: focused, riveted, though focussed, rivetted would be regarded as also correct.

The only letters with obligatory doubling are L and P (traveled, worshiped are definitely Americanisms, not alternative spellings), and with P it's only with worshipping and kidnapping and handicapping, where the syllable has some secondary stress on it and is pronounced with a full vowel.