Efficient conjugate gradient method against BFGS for nonlinear optimization

Question

I am trying to optimize an unconstrained non-convex optimization problem. I know that, in general, BFGS takes fewer iterations than conjugate gradient method but consumes more memory (and hence sometimes more computational time). However, I explicitly want a version of conjugate gradient (with or without preconditioner) such that, it takes fewer iterations as compared to BFGS. I am not much concerned about time and memory consumption, but about fewer function evaluations/gradients as they are costly to evaluate. Is there a method other than these two, which can achieve the desired result ? I have already taken a look into a similar question: https://scicomp.stackexchange.com/questions/507/bfgs-vs-conjugate-gradient-method But they don't propose any new algorithm other than N-GMRES which again depends upon above two procedures.