Cobalt-Rhenium (Co-Re)-based alloys are currently investigated as potential high-temperature materials with melting temperatures beyond those of nickel-based superalloys. Their attraction stems from the binary Co-Re phase diagram, exhibiting complete miscibility between Co and Re, whereby the melting temperature steadily increases with the Re-content. Thus, depending on the Re-content, one can tune the melting temperature between that of pure Co (1495 °C) and that of pure Re (3186 °C). Current investigations focus on Re-contents of about 15 at.%, which makes melting with standard equipment still feasible. In addition to solid solution strengthening due to the mixture of Co- and Re-atoms, particle strengthening by tantalum carbide (TaC) and titanium carbide (TiC) precipitates turned out to be promising in recent studies. Yet, it is currently unclear which of the two particle types is the best choice for high temperature applications nor has the strengthening mechanism associated with the monocarbide (MC)-precipitates been elucidated. To address these issues, we perform compression tests at ambient and elevated temperatures on the particle-free base material containing 15 at.% of rhenium (Re), 5 at.% of chromium (Cr) and cobalt (Co) as balance (Co-15Re-5Cr), as well as on TaC- and TiC-containing variants. Additionally, transmission electron microscopy is used to analyze the shape of the precipitates and their orientation relationship to the matrix. Based on these investigations, we show that TiC and TaC are equally suited for precipitation strengthening of Co-Re-based alloys and identify climb over the elongated particles as a rate controlling particle strengthening mechanism at elevated temperatures. Furthermore, we show that the Re-atoms are remarkably strong obstacles to dislocation motion, which are overcome by thermal activation at elevated temperatures.