A list A = {lambda(1), lambda(2), ... , lambda(n)} of complex numbers is said to be realizable if it is the spectrum of an entrywise nonnegative matrix. The list Lambda is said to be universally realizable (UR) if it is the spectrum of a nonnegative matrix for each possible Jordan canonical form allowed by Lambda. It is well known that an n x n nonnegative matrix A is co-spectral to a nonnegative matrix B with constant row sums. In this paper, we extend the co-spectrality between A and B to a similarity between A and B, when the Perron eigenvalue is simple. We also show that if epsilon >= 0 and A = {lambda(1), lambda(2), ... , lambda(n)} is UR, then {lambda(1)+epsilon , lambda(2), ... , lambda(n)} is also UR. We give counter-examples for the cases: Lambda = {lambda(1), lambda(2), ... , lambda(n)} is UR implies {lambda(1)+epsilon, lambda(2)-epsilon , ... , lambda(n)} is UR, and Lambda(1), Lambda(2) are UR. implies Lambda(1) boolean OR Lambda(2) is UR. (C) 2018 Elsevier Inc. All rights reserved.