Yttrium and rare earth elements (REY) in aqueous environments have been intensively studied because they record important geochemical information. For example, the cerium anomaly, measured in marine sedimentary rocks, has been widely applied as a paleoredox indicator. Marine carbonates are the main substrate used to reconstruct REY signal in paleo-oceans with the underlying assumption that REY incorporated into carbonate minerals preserve the authigenic seawater signal. However, extracting authigenic REY signals from carbonate rocks are challenging. It requires dissolving carbonate phases using acid leaching procedures without contamination from other non-carbonate phases such as Mn/Fe oxides (hydroxides), clay minerals, siliciclastic and organic phases. Multiple dissolution protocols, especially partial leaching, were proposed to eliminate potential contaminations. Yet, the efficiency lof these procedures in reducing contamination remains ambiguous. Additionally, no systematic study on how each non-carbonate phase can modify the authigenic REY signal from carbonates. First, we systematically investigated the efficiency of using ammonium acetate buffer pre-treatment to remove exchangeable ions prior to dissolution. We tested a range of concentration, pH, and reaction time of the buffer and we found that ammonium acetate of 1 M with a pH slightly < 7, and 30 mins for reaction time works best for efficiency. Second, we tested a range of acid species and molarity to dissolve common non-carbonate contamination phases including USGS standards NOD-A-1 (manganese nodule) and SBC-1 (Brush Creek shale), as well as montmorillonite, kaolinite, illite from the Clay Minerals Society. We used three batches of acetic and nitric acids with different molarity and found that both the acid species and molarity are key parameters to avoid leaching of non-carbonate phases. We observed a negative Ce anomaly during leaching of Mn nodule using acetic acid versus a positive anomaly using nitric acid suggesting that nitric acid may introduce false positive Ce anomalies into samples. We also demonstrated that it is essential to filter the leachate to prevent the later dissolution of floating particles. For instance, Mn oxides, which carry positive Ce anomalies, can overprint the carbonate REY signal because the nitric acid (i.e. 2% v/v) used during later ICP-MS analysis could dissolve tetravalent Ce. Third, we conducted a series of leaching experiments on mixed samples consisting of 80% pure modern limestone and 20% mixed pure contaminants to identify the best protocol to avoid contamination. We demonstrate that using acetic acid with a molarity lower than 0.5 M is sufficient to avoid contaminations from Mn oxides, clay minerals, and siliciclastic phases. Finally, we present a new sequential leaching protocol for calcite ( > 75% CaCO3) using two steps of ammonium acetate pre-leaching followed by three steps of 0.3 M acetic acid leaching.