Several modified estimation methods of the memory parameter have been introduced in the past years. They aim to decrease the upward bias of the memory parameter in cases of low frequency contaminations or an additive noise component, especially in situations with a short-memory process being contaminated. In this paper, we provide an overview and compare the performance of nine semiparametric estimation methods. Among them are two standard methods, four modified approaches to account for low frequency contaminations and three procedures developed for perturbed fractional processes. We conduct an extensive Monte Carlo study for a variety of parameter constellations and several DGPs. Furthermore, an empirical application of the log-absolute return series of the S&P 500 shows that the estimation results combined with a long-memory test indicate a spurious long-memory process.