The robust servomechanism problem, also known as the problem of robust output regulation, is considered for a family of uncertain triangular systems. In contrast to the previous work where the uncertain vector field of the controlled plant was assumed to be bounded by a linear growth of the unmeasurable states multiplied by a polynomial function of the system output, we show that the polynomial growth condition can be relaxed and robust output regulation by error feedback is still possible, as long as the uncertain system is dominated by a continuous function of the system output multiplied by a linear growth of the unmeasurable states.