Abundancy ratios are rational numbers k satisfying σ(N)/N = k/m for some N ∈ Z_≥1, where σ is the sum-of-divisors function. In this paper we examine abundancy ratios of the form σ(m)+1 , where gcd(m, σ(m) + 1) = 1. Defining D to be a quasi-friendly divisor of N if σ(N) = σ(D)+1 with D|N, our main results characterize all possible quasi-friendly divisors D having two or more distinct prime divisors and satisfying gcd(D, σ(D) + 1) = 1. In fact, we prove that no such quasi-friendly divisor can have more than two distinct prime divisors.