The MacLane's class A of analytic functions is the class of nonconstant analytic functions in the unit disk that have asymptotic values at a dense subset of the unit circle. In this paper, we define a subclass R of A consisting of those functions that have asymptotic values at a dense subset of the unit circle reached along rectifiable asymptotic paths. We also show that the class R is a proper subclass of A by constructing a function f ∈ A that admits no asymptotic paths of finite length.