Stop minting pennies, nickels, and quarters; start minting 20 cent pieces and mint more 50 cent pieces; let the free market sort it out. I'm not being flippant, it would actually work, at least as far as not wasting money producing low-value coinage is concerned.
Or, just skip the 20 cent and let 10/50 be the only subdivisions. (Currently, we get by with 1/5 and no 2.)
Frankly, if we're talking radical reform I'd rather keep the quarter and ditch the dime; even 10c seems too small to fiddle with most of the time, so 25c is the smallest denomination that seems worth bothering with. (Also, it's ubiquitous in mechanical coin-op devices like laundry machines, pool tables, etc.)