It has been common practice to assume that a 2-parameter Weibull probability distribution is suitable for modeling lumber strength properties. Previous work has demonstrated theoretically and empirically that the modulus of rupture (MOR) distribution of a visual grade of lumber or of lumber that has been binned by modulus of elasticity (MOE) is not a 2-parameter Weibull. Instead, the tails of the MOR distribution are thinned via pseudo-truncation. Simulations have established that fitting 2-parameter Weibulls to pseudo-truncated data via either full or censored data methods can yield poor estimates of probabilities of failure. In this article, we support the simulation results by analyzing large In-Grade type data sets and establishing that 2-parameter Weibull fits yield inflated estimates of the probability of lumber failure when specimens are subjected to loads near allowable properties. In this article, we also discuss the censored data or tail fitting methods permitted under ASTM D5457, Standard Specification for Computing Reference Resistance of Wood-Based Materials and Structural Connections for Load and Resistance Factor Design.