Retail banks usually apply simple linear regression models for describing the dynamics of the deposit rates of non-maturing accounts (NMA) like savings deposits. Thus, typical patterns like asymmetry or rigidity that banks follow when adjusting their deposit rates are ignored. This is insofar surprising, as the asymmetric deposit rate adjustment affects the pricing of embedded options for NMA. In this work we contribute to the elimination of these inconsistencies. Based on data for deposit rates from a representative sample of Swiss banks we provide a strong evidence for both asymmetric adjustment and rigidity pattern. Our proposed modeling approaches reveal that the strategies of Swiss banks to adjust deposit rates are regime dependent. In times of market stress, Swiss banks are tight to market rates; however, in normal regimes this is not observed.