Wandering the aisles of a German home improvement warehouse I found this Bosch EasyCut12 battery powered saw. It is technically a chainsaw but the chain is really tiny with a 2.5" long blade and about 0.06" kerf. I have not seen it on the US market but that may only be a matter of time.
It can do basically what a jigsaw can do with the pro of no vibration and reciprocating action but the con of limited curve radius due to the blade width (and rather expensive blade/chain replacements). Pretty powerful cutting as far as my experiments on hidden areas of my guest quarter's furniture go. I read most people actually use it for bush/tree pruning or detail chainsaw carving.
Anyway, just wanted to share because I find it a cool (if not cute) new toy. I will see back home if it is really useful.