Given any generative classifier based on an inexact density model, we can define a discriminative counterpart that reduces its asymptotic error rate. We introduce a family of classifiers that interpolate the two approaches, thus providing a new way to compare them and giving an estimation procedure whose classification performance is well balanced between the bias of generative classifiers and the variance of discriminative ones. We show that an intermediate trade-off between the two strategies is often preferable, both theoretically and in experiments on real data.