An operator T acting on a Banach space X satises the property (UWE) if \sigma_a(T) n SF \setminus \sigma{SF_+^-} = E(T), where a(T) is the aproximate point spectrum of T, SF_+^-(T) is the upper semi-Weyl spectrum of T and E(T) is the set of all eigenvalues of T that are isolated in the spectrum \sigma(T) of T. In this paper we introduce and study two new spectral properties, namely (V_E) and (V_{Ea} ), in connection with Weyl type theorems. Among other results, we have that T satises property (VE) if and only if T satises property (UWE) and \sigma (T) = \sigma_a (T).