Although the broad Balmer emission line profiles of most optically-selected AGNs appear to have simple logarithmic profiles, some AGNs show asymmetric broad-line profiles with displaced peaks. Suggested causes of these profiles include supermassive binary black holes (Gaskell 1983) and non-axisymmetric continuum emission (Gaskell 2010). We explore here instead the proposal of Gaskell & Harrington (2018) that partial obscuration by dust clouds is a cause of Balmer-line asymmetries. In particular, we investigate whether this model can explain the most extreme Balmer line profiles. We model an unobscured BLR as a tilted, turbulent, flattened distribution of gas, co-rotating above the accretion disk.