I use WTB's All Terrainasaurus on my mtn bike for pavement and light off road use. They look to have a more aggressive tread than slicks/semi slicks but not full mtn bike tires. They don't buzz on the pavement, have good rolling resistance, corner well but also do well in light gravel or dirt. Not sure how well they would do on wet surface because they're rated for moist surface.

I agree with the let some air out. It makes a difference with ride quality and traction.