Tiagra upshifting jumping 3-4 gears in middle of cassette My Tiagra 10-speed shifters have recently been jumping multiple gears. 
Shifting down (from smallest cog to biggest) is fine (10-9-8-7-6-5-4-3-2-1), though maybe a little stiff. But shifting up will jump in the middle (1-2-3-4567-8-9-10) with single pushes of the paddle casing the gears to crash up multiple gears in the middle.

I've ridden 20K miles (32K Km) on this bike. The shifter cable was replaced in May, about 250 miles ago (this is my winter bike), and the rear mech was new in February.

So I'm thinking maybe the shifters are just worn out?

Or should I just replace them? 

Are the shifters serviceable? 

Or could it be something else? I don't think it's cable tension as I'm shifting up fine - but I'm not a mechanic so...) 

Thanks for any good advice.
That sounds like the shifter itself is malfunctioning.

If the cable or derailleur was hanging up you would get delayed multiple upshifts after clicking the lever several times, but you are saying that a single click results in a 3 sprocket upshift. 

My guess is that the pawl mechanism in the shifter has worn and is slipping when upshifting, but is managing to hang on when downshifting. To confirm this you could try detaching the shift cable from the derailleur, putting tension on the cable manually (as close the shifter as possible if you have exposed shift cables, to eliminate cable or housing problems from the test) and seeing if you can get the shifter to slip when upshifting. 

If the shifter is the problem, they are not serviceable. A replacement is necessary.