There is lots of information in Fitfreak-forums, but it's good to remember that they only have 1.5 liter engine in North-America. There are differences between GK Jazz 1.3 and 1.5 engines, although both are L-series DOHC i-VTEC engines. For example 1.3 uses Atkinson-cycle in low rpms but 1.5 not.
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What is the Atkinson-cycle exactly?
Would it be in the 2012 1.3 engine?
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Atkinson cycle leaves the inlet valve open for a short time as the piston rises on the compression stroke, this allows some of the air in the cylinder to escape back into the inlet manifold, this reduces the compression ratio of the engine, obviously reducing power, the amount of fuel injected is also reduced meaning the air / fuel ratio which is normally something like 14.7:1 for full power can be as low as 40:1 or more.