We search for faint CaII lines in the spectra of about 800 apparently single white dwarfs observed at high resolution for the SPY (ESO Supernova Progenitor Survey) survey. Photospheric Ca is detected in 24 DAZ; in 25 mostly hot objects the observed lines must be interstellar. The distribution of metal abundances is discussed and compared with the predictions of the accretion/diffusion scenario. We argue that the observations are easier to understand in a scenario of continuous ongoing accretion with rates varying with the conditions of the ambient medium, rather than with the strongly idealized ``two phase accretion/diffusion scenario'' of Dupuis et al. (1992, 1993a, 1993b).