In this article we deal with robust estimation in linear models of the form: y i =x 1 i 'β 1 +x 2 i 'β 2 +e i (i=1,...,n), in which the x 1 i are fixed 0-1 vectors - such as an ANOVA design - and the x 2 i are continuous random variables which may contain leverage points. Here M estimates are not robust, and S estimates may be too expensive. We propose two types of estimates: one is a weighted L 1 estimate, and the other a combination of M and S estimates, which attains the maximum breakdown point. The consistency and asymptotic normality of both types of estimates are proved. Simulations suggest that the former is better when the dimension of x 2 i is =<3, and the latter when it is >=4, especially for high contamination.