Cellulose fibers are a major industrial input, but due to their irregular shape and anisotropic material response, accurate material characterization is difficult. Single fiber tensile testing is the most popular way to estimate the material properties of individual fibers. However, such tests can only be performed along the axis of the fiber and are associated with problems of enforcing restraints. Alternative indirect approaches, such as micro-mechanical modeling, can help but yield results that are not fully decoupled from the model assumptions. Here, we compare these methods with nanoindentation as a method to extract elastic material constants of the individual fibers. We show that both the longitudinal and the transverse elastic modulus can be determined, additionally enabling the measurement of fiber properties in-situ inside a sheet of paper such that the entire industrial process history is captured. The obtained longitudinal modulus is comparable to traditional methods for larger indents but with a strongly increased scatter as the size of the indentation is decreased further.