Covered bonds are a specific example of senior secured debt. If the issuer of the bonds defaults, the proceeds of the assets in the cover pool are used for their debt service. If in this situation the cover pool proceeds do not suffice for the debt service, the creditors of the bonds have recourse to the issuer's assets and their claims are pari passu with the claims of the creditors of senior unsecured debt. Historically, covered bonds have been very safe investments. During their more than two hundred years in existence, investors never suffered losses due to missed payments from covered bonds. From a risk management perspective, therefore, modeling covered bonds losses is mainly of interest for estimating the impact that the asset encumbrance by the cover pool has on the loss characteristics of the issuer's senior unsecured debt. We explore one period structural modeling approaches for covered bonds and senior unsecured debt losses with one and two asset value variables, respectively. Obviously, two assets models with separate values of the cover pool and the issuer's remaining portfolio allow for more realistic modeling. However, we demonstrate that exact calibration of such models may be impossible. We also investigate a one-asset model in which the riskiness of the cover pool is reflected by a risk-based adjustment of the encumbrance ratio of the issuer's assets.