The Internal Ratings Based (IRB) approach introduced in the Basel II Accord requires financial institutions to estimate not just the probability of default, but also the Loss Given Default (LGD), i.e., the proportion of the outstanding loan that will be lost in the event of a default. However, modelling LGD poses substantial challenges. One of the key problems in building regression models for estimating the loan-level LGD in retail portfolios such as mortgage loans relates to the difficulty of modelling their distributions, as they typically contain extensive numbers of zeroes. In this paper, an alternative approach is proposed where a mixed discrete-continuous model for the total loss amount incurred on a defaulted loan is developed. The model accommodates the probability of a zero loss and the loss amount given that a loss occurs simultaneously. The approach is applied to a large dataset of defaulted home mortgages from a UK bank and compared to two well-known industry approaches. Our zero-adjusted gamma model is shown to present an alternative and competitive approach to LGD modelling.