If you're truly looking for a lens to replace your 15-85, then you should sell the 15-85 to offset the cost of the new lens. If you also buy the replacement lens used or refurbished, you can save even more. That said, it would help us give recommendations if you would tell us the budget for the new lens.
If you are mostly taking issue with the lens performance at 15-20mm, consider supplementing it with a wide-angle fast prime rather than replacing the 15-85 all together. Canon makes a 20mm f2.8, and Sigma makes a 20mm f1.8 (although this is reportedly quite soft at f1.
If you do decide that you need to replace the 15-85, unfortunately I can't think of any lens that's clearly better. The EF-S 17-55 f2.8 IS USM may have f2.8, but I think it suffers from similar vignetting, the focal range is neither as wide nor as long, and the 17-55 is even heavier than the 15-85.
The Canon EF 17-40mm f4L USM, in my opinion, doesn't have enough focal range to be used a general purpose walk-around. Reviews generally suggest that the 17-40 does not suffer from vignetting issues, and it is slightly lighter than the 15-85. Also note that the 15-85 has f4 or better until 26mm, and f4.5 up to 37mm. So the 17-40mm f4 would not be appreciably faster.
The Tamron 17-50mm f2.8 (non VC) may be your best bet. (At approximately $450, you may actually make money if you sell your 15-85 to fund the purchase.) It weighs much less than the 15-85, does not suffer from vignetting issues, has a constant f2.8 aperture, and is reportedly very good optically.