This Tamron lens does indeed do that. It covers not the full range of my lenses, but covers the hearty medium. Precisely, it replaces the kit Canon 17-85mm f4-5.6 IS which previously was the lens I had which covered the greatest area around normal, but always felt lacking on the telephoto end.
The Canon's IS claims about three-stops, and often seemed magical when I used it in conditions that I thought were horridly dark. Tamron claims four-stops, but even on a bright day, shooting at 1/500, it's proven disappointing thus far.
Oddly, coming from only Canon zoom lenses, the zoom ring rotates in the opposite direction. Moreover, it doesn't support full-time manual focus and removing the lens hood is difficult to do without adjusting the focus by accident (but at least it come with a lens hood). The conclusion that I have after a short time with it, is that I don't like it, but it does what I bought it for.