Menthosomes, novel deformable carriers for the enhancement of transdermal delivery are introduced in this study. Meloxicam (MX)-loaded menthosomes were formulated, and their physicochemical characteristics and skin permeability were evaluated. A two-factor spherical and second-order composite experimental design was used to prepare the formulation of the menthosomes. Ten formulations of menthosomes composed of a phospholipid as the lipid bilayer carrier, cholesterol (Chol) as a stabilizer and cetylpyridinium chloride (CPC) and L-menthol as penetration enhancers were prepared. The amounts of Chol and CPC were selected as causal factors. Physicochemical characteristics (particle size, size distribution, zeta potential, elasticity and drug content) and an in vitro skin-permeation study of meloxicam-loaded menthosomes were evaluated. The concentrations of MX that permeated the skin at 2–12 h and the flux were selected as response variables. The optimal formulation was estimated using a nonlinear response-surface method incorporating thin-plate spline interpolation. The experimental values were very close to the values predicted by the computer programs in this study. A Bayesian network analysis was applied to gain a mechanistic understanding of the relationships between causal factors and response variables.