A favourite of mine is using a sin() function instead.
This will have the "unfortunate" side effect of removing
odd harmonics if you take it to the extreme: a triangle
wave gets mapped to a pure sine wave.
This will work with a going from .1 or so to a= 5 and bigger!
The mathematical limits for a = 0 actually turns it into a linear
function at that point, but unfortunately FPUs aren't that good
with calculus :-) Once a goes above 1, you start getting clipping
in addition to the "soft" wave shaping. It starts getting into
more of an effect and less of a mastering tool, though :-)
Seeing as this is just various forms of wave shaping, you
could do it all with a look-up table, too. In my version, that would
get rid of the somewhat-expensive sin() function.