The homogenous copper or copper-based alloy bullet was problematic from the beginning--laying down excessive fouling, boosting pressures via increased friction due to longer bearing surfaces, giving somewhat erratic expansion--but it offered certain advantages (such as incredible penetration and 100-percent weight retention) that made pursuing it worth the trouble.
Though non-lead homogenous bullets are now cropping up from almost every manufacturer, the lion's share of the credit for pioneering a successful homogenous bullet belongs to Barnes Bullets. In fact, through innovations like friction-reducing grooves around the bullet's shank and an aerodynamic plastic tip to ensure reliable expansion, the company has pretty much perfected the copper bullet.
The latest iteration is dubbed the TTSX (Tipped Triple-Shock), and it tends to provide almost match-bullet accuracy in every rifle/caliber I've tried. Sold in boxes of 50, they aren't cheap, but neither is a lost opportunity. The TTSX will help you avoid those.