I have high arches and overpronate a fair amount. These shoes are surprisingly stable, supportive and comfortable. I've  tried many stability and motion control shoes, but either they didn't offer enough resistance to lateral rolling, or they were like wearing bricks. Mizuno seems to have solved these problems: the wave plate offers substantial motion control and support, but the shoe feels light, airy, and responsive. Very well ventilated, so not so good for cold, wet weather running. For that, try their trail shoe, the Cabrakan - it fits like these, but with a burlier tread and weather resistant upper.