My new (second hand) frame has a 150mm tall headtube, what is the minimum length steerer tube i can have? Don't want to buy something off classifieds that won't be suitable.

Cheers

find out the stack height of your headset plus the height of your stem, add the head tube height and subtract 5mm. Will mean running no spacers but that's the min you'll get away with.

Just off the top of my head, a Chris King headset and Thomson stem will have a stack height of about 71.8mm which is about average. For low stack, a CB headset and a FSA stem will have a stack height of about 56mm.

To give yourself a bit of adjustability, with a 150mm headtube, I'd be looking at 230mm+ steerer

Integrated headset, how much will that lose me?

depends ont he headset design – could be bugger al lor anything upto 15mm or so.

Which one have you got?

Cane creek in a BMC elite frame

well google lists a cane creek IS2 as having a stack height of 8.7mm.

call it 15 to be on the safe side and allow for a spacer and add your stem height and subtract 5mm.