In this article we consider the class A(p) which consists of functions that are meromorphic in the unit disc D having a simple pole at z = p ∈ (0, 1) with the normalization f(0) = 0 = f′ (0)−1. First we prove some sufficient conditions for univalence of such functions in D. One of these conditions enable us to consider the class Vp(λ) that consists of functions satisfying certain differential inequality which forces univalence of such functions. Next we establish that (Formula presented), where Up(λ) was introduced and studied in [2]. Finally, we discuss some coefficient problems for Vp(λ) and end the article with a coefficient conjecture.