The recent update of Eurocode 6 (EC6) undertaken by the Technical Committee “CEN/TC 250/SC 6” was an opportunity to reevaluate the verification techniques for unreinforced masonry (URM) walls when exposed to combined vertical and out-of-plane (OOP) loading, along with significant second-order effects. The approach provided in the prior edition of EC6 relied on a reduction factor for axial load capacity (ϕm) derived from an approximate model, which was quite conservative for a broad spectrum of wall stiffnesses. Furthermore, in the earlier edition of EC6, there was no need for a specific verification of lateral flexural capacity for URM walls exposed to substantial OOP lateral forces, such as seismic actions. Instead, this verification would be appropriate and rational. To address this verification, which should also consider second-order effects, a reduction factor analogous to ϕm can be established for the reduction in bending capacity (ϕM). Hence, the primary objective of this paper is to present the scientific derivation of the updated criteria implemented in the current edition of EC6 (EN1996-1-1:2022) for assessing second-order effects in URM walls. Specifically, this paper outlines the numerical method used to quantify the ϕ factors, which has led to an enhancement of the estimates previously found in the literature. Based on these numerical findings, prediction models for the ϕ factors are proposed. These models are utilized to illustrate the direct relationship between ϕm and ϕM. Subsequently, validation comparisons between the predicted ϕ values and the corresponding experimental and numerical values from existing literature are shown. Finally, the calibration of the newly introduced ϕm and ϕM models in the latest edition of EC6 is presented.