Optimized search for yield-to-worst of a callable bond

Question

Suppose that I need to find the yield-to-worst of a callable bond, and that the option is American (call any time). The bond may have step-up coupons and/or non-constant call price (oprion strike). Brute force calculation of the yield-to-call for every possible call date can take a long time. Is there any way to speed up this search? I was thinking of something similar to Newtorn-Raphson or Brent in spirit.